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    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Related Party [Axis]</link:label>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities_088cb7a7-7f51-4d88-b71b-a50ef3eb2113_verboseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Change in accounts payable and accrued expenses</link:label>
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    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_5cdcdb7a-f4f8-4703-8fbf-317f51b347cf_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Significant Unobservable Inputs (Level 3)</link:label>
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    <link:label id="lab_hgit_DebtWeightedAverageYearstoMaturity_8b15aef5-c44a-4112-879c-c85457e37f0c_terseLabel_en-US" xlink:label="lab_hgit_DebtWeightedAverageYearstoMaturity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt, weighted average years to maturity</link:label>
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    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_6df758c4-f44e-4b41-bd92-096a57f6fcce_verboseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">LIABILITIES AND EQUITY</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Liabilities and Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_LiabilitiesAndStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditMember_8b6d37c3-7ef4-4027-b42b-78344539aa33_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Line of Credit</link:label>
    <link:label id="lab_us-gaap_LineOfCreditMember_label_en-US" xlink:label="lab_us-gaap_LineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Line of Credit [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditMember" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_LineOfCreditMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditMember" xlink:to="lab_us-gaap_LineOfCreditMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFiveYears_f545265f-3fdf-4755-b56b-f139fd3b8f83_terseLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFiveYears" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">2025</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFiveYears_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFiveYears" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFiveYears" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceivedFiveYears"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFiveYears" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFiveYears" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_RentReliefProvidedToTenantsByAbatement_b8385067-63d4-4bd8-bef8-96a2237a085a_terseLabel_en-US" xlink:label="lab_hgit_RentReliefProvidedToTenantsByAbatement" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Rent relief provided to tenants, by abatement</link:label>
    <link:label id="lab_hgit_RentReliefProvidedToTenantsByAbatement_label_en-US" xlink:label="lab_hgit_RentReliefProvidedToTenantsByAbatement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Rent relief provided to tenants, by abatement</link:label>
    <link:label id="lab_hgit_RentReliefProvidedToTenantsByAbatement_documentation_en-US" xlink:label="lab_hgit_RentReliefProvidedToTenantsByAbatement" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Rental payments that were forgiven or reduced due to the conversion of fixed rental payments to rental payments based on a percentage of the tenant&#8217;s revenues.</link:label>
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    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThereafter_b45da090-8532-48c5-bf3c-f4ed7d8d21b1_terseLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThereafter" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThereafter_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThereafter" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, after Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThereafter" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceivedThereafter"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThereafter" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThereafter" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_e6e09e9e-002b-4254-8e33-9f3ffd2c538e_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">DERIVATIVE INSTRUMENTS</link:label>
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    <link:label id="lab_hgit_CommonClassDMember_da9959c6-b743-4021-a1b7-628b53603a8f_terseLabel_en-US" xlink:label="lab_hgit_CommonClassDMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Class D</link:label>
    <link:label id="lab_hgit_CommonClassDMember_label_en-US" xlink:label="lab_hgit_CommonClassDMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Class D [Member]</link:label>
    <link:label id="lab_hgit_CommonClassDMember_documentation_en-US" xlink:label="lab_hgit_CommonClassDMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Class D [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_CommonClassDMember" xlink:href="hgit-20200930.xsd#hgit_CommonClassDMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_CommonClassDMember" xlink:to="lab_hgit_CommonClassDMember" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_InternationalResidentialLivingInvestmentsMember_22fa145f-73b2-471c-8b8e-3b8770b0d0f3_terseLabel_en-US" xlink:label="lab_hgit_InternationalResidentialLivingInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">International residential/living investments</link:label>
    <link:label id="lab_hgit_InternationalResidentialLivingInvestmentsMember_label_en-US" xlink:label="lab_hgit_InternationalResidentialLivingInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">International Residential/Living Investments [Member]</link:label>
    <link:label id="lab_hgit_InternationalResidentialLivingInvestmentsMember_documentation_en-US" xlink:label="lab_hgit_InternationalResidentialLivingInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">International Residential/Living Investments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_InternationalResidentialLivingInvestmentsMember" xlink:href="hgit-20200930.xsd#hgit_InternationalResidentialLivingInvestmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_InternationalResidentialLivingInvestmentsMember" xlink:to="lab_hgit_InternationalResidentialLivingInvestmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_RelatedPartyPerformanceParticipationAllocationPercentageOfAnnualReturn_e71265f8-3c4d-4865-8649-6e6ff6e8538f_terseLabel_en-US" xlink:label="lab_hgit_RelatedPartyPerformanceParticipationAllocationPercentageOfAnnualReturn" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Related party allocation percentage of annual total return</link:label>
    <link:label id="lab_hgit_RelatedPartyPerformanceParticipationAllocationPercentageOfAnnualReturn_label_en-US" xlink:label="lab_hgit_RelatedPartyPerformanceParticipationAllocationPercentageOfAnnualReturn" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Related Party Performance Participation Allocation Percentage Of Annual Return</link:label>
    <link:label id="lab_hgit_RelatedPartyPerformanceParticipationAllocationPercentageOfAnnualReturn_documentation_en-US" xlink:label="lab_hgit_RelatedPartyPerformanceParticipationAllocationPercentageOfAnnualReturn" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Related Party Performance Participation Allocation Percentage Of Annual Return</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_RelatedPartyPerformanceParticipationAllocationPercentageOfAnnualReturn" xlink:href="hgit-20200930.xsd#hgit_RelatedPartyPerformanceParticipationAllocationPercentageOfAnnualReturn"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_RelatedPartyPerformanceParticipationAllocationPercentageOfAnnualReturn" xlink:to="lab_hgit_RelatedPartyPerformanceParticipationAllocationPercentageOfAnnualReturn" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableRateDomain_ffff3eea-a4ac-403d-82fb-110791a6ce13_terseLabel_en-US" xlink:label="lab_us-gaap_VariableRateDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Variable Rate [Domain]</link:label>
    <link:label id="lab_us-gaap_VariableRateDomain_label_en-US" xlink:label="lab_us-gaap_VariableRateDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Variable Rate [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableRateDomain" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_VariableRateDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableRateDomain" xlink:to="lab_us-gaap_VariableRateDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableRateAxis_42b25724-4bb5-4ccd-9465-03ad4faefe0a_terseLabel_en-US" xlink:label="lab_us-gaap_VariableRateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Variable Rate [Axis]</link:label>
    <link:label id="lab_us-gaap_VariableRateAxis_label_en-US" xlink:label="lab_us-gaap_VariableRateAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Variable Rate [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableRateAxis" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_VariableRateAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableRateAxis" xlink:to="lab_us-gaap_VariableRateAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_401fc95c-c9db-45c6-8766-4c5dbeb3a85b_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Business Acquisitions, by Acquisition [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Business Acquisitions, by Acquisition [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:to="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis_a2305e11-2570-4bd3-adb7-08f99ae60bc8_terseLabel_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Real Estate, Type of Property [Axis]</link:label>
    <link:label id="lab_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis_label_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Real Estate, Type of Property [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis" xlink:href="http://xbrl.fasb.org/srt/2020/elts/srt-2020-01-31.xsd#srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis"/>
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    <link:label id="lab_us-gaap_CommitmentsAndContingencies_550fc03d-a185-4696-b0ac-3342f462f49f_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commitments and contingencies (Note 11)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingencies" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_CommitmentsAndContingencies"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingencies" xlink:to="lab_us-gaap_CommitmentsAndContingencies" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForRepurchaseOfCommonStock_cd719294-70d6-4bff-9bf2-b456bf39067d_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Redemption of common shares</link:label>
    <link:label id="lab_us-gaap_PaymentsForRepurchaseOfCommonStock_label_en-US" xlink:label="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments for Repurchase of Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_PaymentsForRepurchaseOfCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:to="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsAbstract_604d9725-1790-4a8f-afeb-948b2ee73b0d_verboseLabel_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">ASSETS</link:label>
    <link:label id="lab_us-gaap_AssetsAbstract_81662efa-9b7d-47e8-8d32-7981f18c6987_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total Assets</link:label>
    <link:label id="lab_us-gaap_AssetsAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsAbstract" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_AssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsAbstract" xlink:to="lab_us-gaap_AssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_1ae66e2b-9576-4d12-9484-f46ce05c6286_terseLabel_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_label_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountingPoliciesAbstract" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_AccountingPoliciesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountingPoliciesAbstract" xlink:to="lab_us-gaap_AccountingPoliciesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressStateOrProvince_8b096073-9475-4e5f-beef-9253b8077d97_terseLabel_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:label id="lab_dei_EntityAddressStateOrProvince_label_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressStateOrProvince" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_EntityAddressStateOrProvince"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressStateOrProvince" xlink:to="lab_dei_EntityAddressStateOrProvince" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BelowMarketLeaseNetAbstract_65e4c1e8-043a-420e-9ab0-93c7e1a6bc8e_terseLabel_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseNetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Out-of-Market Lease Liabilities</link:label>
    <link:label id="lab_us-gaap_BelowMarketLeaseNetAbstract_label_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseNetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Below Market Lease, Net [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BelowMarketLeaseNetAbstract" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_BelowMarketLeaseNetAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BelowMarketLeaseNetAbstract" xlink:to="lab_us-gaap_BelowMarketLeaseNetAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_NumberOfPropertiesHeldForSale_75fd938d-c46d-44bc-bec5-382ad9fae56c_terseLabel_en-US" xlink:label="lab_hgit_NumberOfPropertiesHeldForSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Number of properties held for sale</link:label>
    <link:label id="lab_hgit_NumberOfPropertiesHeldForSale_label_en-US" xlink:label="lab_hgit_NumberOfPropertiesHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Number Of Properties Held For Sale</link:label>
    <link:label id="lab_hgit_NumberOfPropertiesHeldForSale_documentation_en-US" xlink:label="lab_hgit_NumberOfPropertiesHeldForSale" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Number Of Properties Held For Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_NumberOfPropertiesHeldForSale" xlink:href="hgit-20200930.xsd#hgit_NumberOfPropertiesHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_NumberOfPropertiesHeldForSale" xlink:to="lab_hgit_NumberOfPropertiesHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_501f86be-34bf-4bf9-ac87-d183261ac272_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">2023</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Long-Term Debt, Maturity, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_ExpenseReimbursementsMember_2103c9c1-9590-4244-ab9e-62972dfdd34e_terseLabel_en-US" xlink:label="lab_hgit_ExpenseReimbursementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Expense Reimbursements</link:label>
    <link:label id="lab_hgit_ExpenseReimbursementsMember_label_en-US" xlink:label="lab_hgit_ExpenseReimbursementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Expense Reimbursements [Member]</link:label>
    <link:label id="lab_hgit_ExpenseReimbursementsMember_documentation_en-US" xlink:label="lab_hgit_ExpenseReimbursementsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Expense Reimbursements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_ExpenseReimbursementsMember" xlink:href="hgit-20200930.xsd#hgit_ExpenseReimbursementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_ExpenseReimbursementsMember" xlink:to="lab_hgit_ExpenseReimbursementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_PercentageofAssetsbasedonAppraisalvalues_4309bd8c-37b3-4cbb-b573-42e893ba4c34_terseLabel_en-US" xlink:label="lab_hgit_PercentageofAssetsbasedonAppraisalvalues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Percentage of assets based on appraisal values</link:label>
    <link:label id="lab_hgit_PercentageofAssetsbasedonAppraisalvalues_label_en-US" xlink:label="lab_hgit_PercentageofAssetsbasedonAppraisalvalues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Percentage of Assets based on Appraisal values</link:label>
    <link:label id="lab_hgit_PercentageofAssetsbasedonAppraisalvalues_documentation_en-US" xlink:label="lab_hgit_PercentageofAssetsbasedonAppraisalvalues" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Percentage of Assets based on Appraisal values</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_PercentageofAssetsbasedonAppraisalvalues" xlink:href="hgit-20200930.xsd#hgit_PercentageofAssetsbasedonAppraisalvalues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_PercentageofAssetsbasedonAppraisalvalues" xlink:to="lab_hgit_PercentageofAssetsbasedonAppraisalvalues" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedRemainderOfFiscalYear_28638608-0de8-4c9a-a55c-6e073e74efb6_terseLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">October 1, 2020 through December 31, 2020</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedRemainderOfFiscalYear" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceivedRemainderOfFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedRemainderOfFiscalYear" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedRemainderOfFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfLinesOfCredit_ffe6005a-c67a-41bd-844a-23874b2f271d_terseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfLinesOfCredit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Repayments of lines of credit</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfLinesOfCredit_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfLinesOfCredit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Repayments of Lines of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfLinesOfCredit" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_RepaymentsOfLinesOfCredit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfLinesOfCredit" xlink:to="lab_us-gaap_RepaymentsOfLinesOfCredit" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_BratzlerABCWestlandMember_7448e945-cfe9-4af9-9ded-8be3fda64cf2_terseLabel_en-US" xlink:label="lab_hgit_BratzlerABCWestlandMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Bratzler ABC Westland</link:label>
    <link:label id="lab_hgit_BratzlerABCWestlandMember_label_en-US" xlink:label="lab_hgit_BratzlerABCWestlandMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Bratzler ABC Westland [Member]</link:label>
    <link:label id="lab_hgit_BratzlerABCWestlandMember_documentation_en-US" xlink:label="lab_hgit_BratzlerABCWestlandMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Bratzler ABC Westland [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_BratzlerABCWestlandMember" xlink:href="hgit-20200930.xsd#hgit_BratzlerABCWestlandMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_BratzlerABCWestlandMember" xlink:to="lab_hgit_BratzlerABCWestlandMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_28985d27-a462-403f-be8e-8af840fa4c55_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Right-of-use asset, net</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Operating Lease, Right-of-Use Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_OperatingLeaseRightOfUseAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:to="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_NumberOfRealEstateInvestments_f49b2619-99e8-4f44-aba9-ea2ba64f6a5f_terseLabel_en-US" xlink:label="lab_hgit_NumberOfRealEstateInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Number of real estate properties</link:label>
    <link:label id="lab_hgit_NumberOfRealEstateInvestments_label_en-US" xlink:label="lab_hgit_NumberOfRealEstateInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Number of Real Estate Investments</link:label>
    <link:label id="lab_hgit_NumberOfRealEstateInvestments_documentation_en-US" xlink:label="lab_hgit_NumberOfRealEstateInvestments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">The number of real estate investments (including real estate properties and other real estate related investments/projects) the entity has interests in as of the balance sheet date.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_NumberOfRealEstateInvestments" xlink:href="hgit-20200930.xsd#hgit_NumberOfRealEstateInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_NumberOfRealEstateInvestments" xlink:to="lab_hgit_NumberOfRealEstateInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract_f95e4d95-2a0b-4ed5-9b37-f6c4b637b426_verboseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Equity:</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Stockholders' Equity, Including Portion Attributable to Noncontrolling Interest [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:to="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromRelatedPartyDebt_e378e205-e03e-4af6-b712-0999d0dd2321_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromRelatedPartyDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from related party note payable</link:label>
    <link:label id="lab_us-gaap_ProceedsFromRelatedPartyDebt_label_en-US" xlink:label="lab_us-gaap_ProceedsFromRelatedPartyDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from Related Party Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromRelatedPartyDebt" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ProceedsFromRelatedPartyDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromRelatedPartyDebt" xlink:to="lab_us-gaap_ProceedsFromRelatedPartyDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_CommonClassIMember_d1dd52c2-a95f-46cc-8482-433cc4b07f05_terseLabel_en-US" xlink:label="lab_hgit_CommonClassIMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Class I</link:label>
    <link:label id="lab_hgit_CommonClassIMember_label_en-US" xlink:label="lab_hgit_CommonClassIMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Class I [Member]</link:label>
    <link:label id="lab_hgit_CommonClassIMember_documentation_en-US" xlink:label="lab_hgit_CommonClassIMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Class I [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_CommonClassIMember" xlink:href="hgit-20200930.xsd#hgit_CommonClassIMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_CommonClassIMember" xlink:to="lab_hgit_CommonClassIMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockValue_e1a52a10-1365-4c98-8253-c700ad1082b0_verboseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred shares, $0.001 par value per share; 500,000 preferred shares authorized, none issued or outstanding as of September&#160;30, 2020 and December&#160;31, 2019</link:label>
    <link:label id="lab_us-gaap_PreferredStockValue_label_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockValue" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_PreferredStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockValue" xlink:to="lab_us-gaap_PreferredStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HedgingDesignationDomain_be4f4b31-3206-48b4-bcb9-0a8b1eaca3d5_terseLabel_en-US" xlink:label="lab_us-gaap_HedgingDesignationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Hedging Designation [Domain]</link:label>
    <link:label id="lab_us-gaap_HedgingDesignationDomain_label_en-US" xlink:label="lab_us-gaap_HedgingDesignationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Hedging Designation [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgingDesignationDomain" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_HedgingDesignationDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HedgingDesignationDomain" xlink:to="lab_us-gaap_HedgingDesignationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_f34857f5-4c86-45c7-8571-cf5ff765b34e_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common stock, par value (in dollars per share)</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_MadridAirportComplexMember" xlink:to="lab_hgit_MadridAirportComplexMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementLineItems_6958c9a5-74cf-43dc-8bb4-51f029bb2073_terseLabel_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statement</link:label>
    <link:label id="lab_us-gaap_StatementLineItems_label_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementLineItems" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_StatementLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementLineItems" xlink:to="lab_us-gaap_StatementLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfStockDomain_32acc257-c67a-4ee8-8fcf-3d83326adaad_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockDomain_label_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ClassOfStockDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfStockDomain" xlink:to="lab_us-gaap_ClassOfStockDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireRealEstateHeldForInvestment_3f788767-f067-45b8-9e33-99c627762a9c_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireRealEstateHeldForInvestment" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Investments in acquired properties and lease intangibles</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireRealEstateHeldForInvestment_8fa20e39-2235-4e90-9cb6-5c575f01bcf6_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireRealEstateHeldForInvestment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract purchase price</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireRealEstateHeldForInvestment_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireRealEstateHeldForInvestment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments to Acquire Real Estate Held-for-investment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireRealEstateHeldForInvestment" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_PaymentsToAcquireRealEstateHeldForInvestment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireRealEstateHeldForInvestment" xlink:to="lab_us-gaap_PaymentsToAcquireRealEstateHeldForInvestment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts_f3d47013-58bf-4100-b748-1784ea5aa0d6_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Acquisition related expenses</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Business Combination, Acquisition Related Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_BusinessCombinationAcquisitionRelatedCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:to="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementTable_af0a5fb7-a4bc-4128-a2f9-3994077d6777_terseLabel_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statement [Table]</link:label>
    <link:label id="lab_us-gaap_StatementTable_label_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statement [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementTable" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_StatementTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementTable" xlink:to="lab_us-gaap_StatementTable" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_HinesCreditFacilityMember_7bdfe6c9-efa6-4e48-8df3-11b14d82ce90_terseLabel_en-US" xlink:label="lab_hgit_HinesCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Hines Credit Facility</link:label>
    <link:label id="lab_hgit_HinesCreditFacilityMember_label_en-US" xlink:label="lab_hgit_HinesCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Hines Credit Facility [Member]</link:label>
    <link:label id="lab_hgit_HinesCreditFacilityMember_documentation_en-US" xlink:label="lab_hgit_HinesCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">A credit facility between Hines Global REIT II, Inc. and Hines Interests Limited Partnership.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_HinesCreditFacilityMember" xlink:href="hgit-20200930.xsd#hgit_HinesCreditFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_HinesCreditFacilityMember" xlink:to="lab_hgit_HinesCreditFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditFacilityAxis_0cb8e94c-b6f2-4902-9168-61a542efce01_terseLabel_en-US" xlink:label="lab_us-gaap_CreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Credit Facility [Axis]</link:label>
    <link:label id="lab_us-gaap_CreditFacilityAxis_label_en-US" xlink:label="lab_us-gaap_CreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Credit Facility [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityAxis" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_CreditFacilityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditFacilityAxis" xlink:to="lab_us-gaap_CreditFacilityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_country_IE_d12e4cf7-79f8-4dbe-961f-74d4fb737688_terseLabel_en-US" xlink:label="lab_country_IE" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Ireland</link:label>
    <link:label id="lab_country_IE_label_en-US" xlink:label="lab_country_IE" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">IRELAND</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_country_IE" xlink:href="https://xbrl.sec.gov/country/2020/country-2020-01-31.xsd#country_IE"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_country_IE" xlink:to="lab_country_IE" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesIssued_73d53786-fb26-4728-bd72-d4c61b77a33a_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred stock, shares issued</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Shares Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesIssued" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_PreferredStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesIssued" xlink:to="lab_us-gaap_PreferredStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceived_eaeb3fb6-b98a-428f-adfc-fe6921569539_totalLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceived" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceived_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceived" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Lessor, Operating Lease, Payments to be Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceived" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceived"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceived" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceived" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_DomesticOfficeRealEstateInvestmentsMember_0f760cfc-d2e0-479f-a11d-6d29485ef560_terseLabel_en-US" xlink:label="lab_hgit_DomesticOfficeRealEstateInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Domestic office investments</link:label>
    <link:label id="lab_hgit_DomesticOfficeRealEstateInvestmentsMember_label_en-US" xlink:label="lab_hgit_DomesticOfficeRealEstateInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Domestic Office Real Estate Investments [Member]</link:label>
    <link:label id="lab_hgit_DomesticOfficeRealEstateInvestmentsMember_documentation_en-US" xlink:label="lab_hgit_DomesticOfficeRealEstateInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Domestic Office Real Estate Investments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_DomesticOfficeRealEstateInvestmentsMember" xlink:href="hgit-20200930.xsd#hgit_DomesticOfficeRealEstateInvestmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_DomesticOfficeRealEstateInvestmentsMember" xlink:to="lab_hgit_DomesticOfficeRealEstateInvestmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementsNonrecurringMember_4a75029e-1129-4f33-94ae-e988f1f1cc30_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsNonrecurringMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value Measurements Nonrecurring</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsNonrecurringMember_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsNonrecurringMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value, Nonrecurring [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsNonrecurringMember" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_FairValueMeasurementsNonrecurringMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementsNonrecurringMember" xlink:to="lab_us-gaap_FairValueMeasurementsNonrecurringMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareBasicAndDiluted_3e346760-2211-4caa-8d27-ba83e2bd8da7_verboseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasicAndDiluted" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Basic and diluted income (loss) per common share (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasicAndDiluted_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasicAndDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Earnings Per Share, Basic and Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasicAndDiluted" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_EarningsPerShareBasicAndDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareBasicAndDiluted" xlink:to="lab_us-gaap_EarningsPerShareBasicAndDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntitySmallBusiness_5abf134b-6f71-42e1-9d97-6532f43369bc_terseLabel_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Small Business</link:label>
    <link:label id="lab_dei_EntitySmallBusiness_label_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Small Business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntitySmallBusiness" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_EntitySmallBusiness"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntitySmallBusiness" xlink:to="lab_dei_EntitySmallBusiness" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_FirstAndSecondOfferingsMember_9e7524d6-a1bf-4cec-b378-995b7935949d_terseLabel_en-US" xlink:label="lab_hgit_FirstAndSecondOfferingsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">First and Second Offerings</link:label>
    <link:label id="lab_hgit_FirstAndSecondOfferingsMember_label_en-US" xlink:label="lab_hgit_FirstAndSecondOfferingsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">First And Second Offerings [Member]</link:label>
    <link:label id="lab_hgit_FirstAndSecondOfferingsMember_documentation_en-US" xlink:label="lab_hgit_FirstAndSecondOfferingsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">First And Second Offerings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_FirstAndSecondOfferingsMember" xlink:href="hgit-20200930.xsd#hgit_FirstAndSecondOfferingsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_FirstAndSecondOfferingsMember" xlink:to="lab_hgit_FirstAndSecondOfferingsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_f4f29990-9de9-43e6-aa8e-79feb4ed01e0_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Increase (Decrease) in Stockholders' Equity</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_IncreaseDecreaseInStockholdersEquityRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:to="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_LeasingFeeMember_3e719897-2c74-4dc2-aa62-d372d99c446b_terseLabel_en-US" xlink:label="lab_hgit_LeasingFeeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Leasing Fee</link:label>
    <link:label id="lab_hgit_LeasingFeeMember_label_en-US" xlink:label="lab_hgit_LeasingFeeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Leasing Fee [Member]</link:label>
    <link:label id="lab_hgit_LeasingFeeMember_documentation_en-US" xlink:label="lab_hgit_LeasingFeeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Leasing Fee [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_LeasingFeeMember" xlink:href="hgit-20200930.xsd#hgit_LeasingFeeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_LeasingFeeMember" xlink:to="lab_hgit_LeasingFeeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_NoncashOfferingCostsPayable_bd12d93d-8107-42ca-bf15-707d9639db0e_terseLabel_en-US" xlink:label="lab_hgit_NoncashOfferingCostsPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Offering costs payable to the Advisor</link:label>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInDueToAffiliates_d9b5d9c1-0ac5-49d6-8472-04d097dc9be1_verboseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInDueToAffiliates" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Change in due to affiliates</link:label>
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    <link:label id="lab_hgit_ABCWestlandMember_8e11112b-3c4c-4e6c-9a9c-42f9245cb041_terseLabel_en-US" xlink:label="lab_hgit_ABCWestlandMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">ABC Westland</link:label>
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    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_20bab0e5-9ddf-4c21-bb1e-e195e14a7570_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value Measurements Fair Value Hierarchy Domain</link:label>
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    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_b3b76530-3df4-4bd1-b57f-25653e991b72_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">DEBT FINANCING</link:label>
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    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfCommonStock_1d014382-be24-46be-b05d-0833d6fa53d5_verboseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from issuance of common shares</link:label>
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    <link:label id="lab_us-gaap_OtherOwnershipInterestsLineItems_b2eb11cb-ba71-4fef-8ce5-b217faca89c4_terseLabel_en-US" xlink:label="lab_us-gaap_OtherOwnershipInterestsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Distributions [Line Items]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherOwnershipInterestsLineItems" xlink:to="lab_us-gaap_OtherOwnershipInterestsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfForeignExchangeContractsStatementOfFinancialPositionTableTextBlock_3772cfd9-75cb-4bec-843e-098d2affc15f_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfForeignExchangeContractsStatementOfFinancialPositionTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Foreign Exchange Contracts</link:label>
    <link:label id="lab_us-gaap_ScheduleOfForeignExchangeContractsStatementOfFinancialPositionTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfForeignExchangeContractsStatementOfFinancialPositionTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Foreign Exchange Contracts, Statement of Financial Position [Table Text Block]</link:label>
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    <link:label id="lab_dei_AmendmentFlag_5d7ecb2e-d550-4251-acc7-e039879a4b56_terseLabel_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Amendment Flag</link:label>
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    <link:label id="lab_hgit_Contract2Member_f001fca9-17f4-406f-b503-3908c61ad938_terseLabel_en-US" xlink:label="lab_hgit_Contract2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Foreign exchange forward contract</link:label>
    <link:label id="lab_hgit_Contract2Member_label_en-US" xlink:label="lab_hgit_Contract2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract 2 [Member]</link:label>
    <link:label id="lab_hgit_Contract2Member_documentation_en-US" xlink:label="lab_hgit_Contract2Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract 2 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_Contract2Member" xlink:href="hgit-20200930.xsd#hgit_Contract2Member"/>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_8a3b5474-00ab-4b1a-bcb5-6b03ba68fcf6_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Finite-Lived Intangible Assets, Major Class Name [Domain]</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Finite-Lived Intangible Assets, Major Class Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstatePropertiesDomain_868cc5f5-d6ac-40c6-9f64-b4befe932860_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstatePropertiesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Real Estate Properties [Domain]</link:label>
    <link:label id="lab_us-gaap_RealEstatePropertiesDomain_label_en-US" xlink:label="lab_us-gaap_RealEstatePropertiesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Real Estate Properties [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstatePropertiesDomain" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_RealEstatePropertiesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstatePropertiesDomain" xlink:to="lab_us-gaap_RealEstatePropertiesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock_a0aa6048-d592-4a93-b30b-5d27cc5cb74d_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule Of Recognized Identified Assets Acquired And Liabilities Assumed</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Recognized Identified Assets Acquired and Liabilities Assumed [Table Text Block]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CorporateNonSegmentMember_0169148e-5b1b-429e-8d45-636b8780b849_terseLabel_en-US" xlink:label="lab_us-gaap_CorporateNonSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Corporate-level accounts</link:label>
    <link:label id="lab_us-gaap_CorporateNonSegmentMember_label_en-US" xlink:label="lab_us-gaap_CorporateNonSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Corporate, Non-Segment [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CorporateNonSegmentMember" xlink:to="lab_us-gaap_CorporateNonSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisTextBlock_168e742a-fb09-4de0-8ad2-4236fb1b5185_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisTextBlock" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisTextBlock"/>
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    <link:label id="lab_us-gaap_BelowMarketLeaseAmortizationIncomeYearTwo_d023c058-6909-4d93-b02e-5726d0594d3b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseAmortizationIncomeYearTwo" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">2022</link:label>
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    <link:label id="lab_us-gaap_LineOfCredit_34dcd2af-62ab-4cf7-aafd-b5b92e9d6e85_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCredit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Outstanding balance</link:label>
    <link:label id="lab_us-gaap_LineOfCredit_label_en-US" xlink:label="lab_us-gaap_LineOfCredit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Long-term Line of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCredit" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_LineOfCredit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCredit" xlink:to="lab_us-gaap_LineOfCredit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ForeignCurrencyExchangeRateTranslation1_cdf263e7-8d17-45b2-b0e0-d7da43fd9c48_verboseLabel_en-US" xlink:label="lab_us-gaap_ForeignCurrencyExchangeRateTranslation1" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Traded currency rate</link:label>
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    <link:label id="lab_us-gaap_ForeignCurrencyExchangeRateTranslation1_label_en-US" xlink:label="lab_us-gaap_ForeignCurrencyExchangeRateTranslation1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Foreign Currency Exchange Rate, Translation</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ForeignCurrencyExchangeRateTranslation1" xlink:to="lab_us-gaap_ForeignCurrencyExchangeRateTranslation1" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_TheEmersonMember_92970ac5-8a39-44d5-a9c3-e42e119730b1_terseLabel_en-US" xlink:label="lab_hgit_TheEmersonMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">The Emerson</link:label>
    <link:label id="lab_hgit_TheEmersonMember_label_en-US" xlink:label="lab_hgit_TheEmersonMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">The Emerson [Member]</link:label>
    <link:label id="lab_hgit_TheEmersonMember_documentation_en-US" xlink:label="lab_hgit_TheEmersonMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">The Emerson [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_TheEmersonMember" xlink:to="lab_hgit_TheEmersonMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfDebt_9d11f50b-4a33-4e4f-aeb1-23bb098300af_terseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Repayments of debt</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfDebt_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Repayments of Debt</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfDebt" xlink:to="lab_us-gaap_RepaymentsOfDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_country_ES_8525ccb9-2823-48d9-afa2-a8f3ac7622aa_terseLabel_en-US" xlink:label="lab_country_ES" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Spain</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_country_ES" xlink:to="lab_country_ES" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesTradingUnrealizedGainLoss_51306734-ddc5-4b1d-b9cc-bf0e71d7596d_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesTradingUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Unrealized gain (loss)</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesTradingUnrealizedGainLoss" xlink:to="lab_us-gaap_DebtSecuritiesTradingUnrealizedGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfRelatedPartyDebt_0c9b0816-e2fa-46ea-8850-1452c7bafcf7_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfRelatedPartyDebt" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments on related party note payable</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfRelatedPartyDebt_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfRelatedPartyDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Repayments of Related Party Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfRelatedPartyDebt" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_RepaymentsOfRelatedPartyDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfRelatedPartyDebt" xlink:to="lab_us-gaap_RepaymentsOfRelatedPartyDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BelowMarketLeaseAmortizationIncomeYearThree_5ea9414a-fa86-4c7e-bbc5-54f180400e75_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseAmortizationIncomeYearThree" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">2023</link:label>
    <link:label id="lab_us-gaap_BelowMarketLeaseAmortizationIncomeYearThree_label_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseAmortizationIncomeYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Below Market Lease, Amortization Income, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BelowMarketLeaseAmortizationIncomeYearThree" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_BelowMarketLeaseAmortizationIncomeYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BelowMarketLeaseAmortizationIncomeYearThree" xlink:to="lab_us-gaap_BelowMarketLeaseAmortizationIncomeYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_6dfec51d-a640-4a70-bd27-f6f89939e0a1_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net cash from (used in) operating activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net Cash Provided by (Used in) Operating Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
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    <link:label id="lab_dei_EntityCentralIndexKey_4f90d431-d592-4bf5-8598-74056faae694_terseLabel_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:label id="lab_dei_EntityCentralIndexKey_label_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Central Index Key</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCentralIndexKey" xlink:to="lab_dei_EntityCentralIndexKey" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyDomain_7d3a6bee-c75e-42ca-81f3-5eea0e7fa2a7_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Related Party [Domain]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyDomain_label_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Related Party [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyDomain" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_RelatedPartyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyDomain" xlink:to="lab_us-gaap_RelatedPartyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByMeasurementFrequencyAxis_6a820dec-843d-4ce6-92f5-05bead04f481_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value By Measurement Frequency [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByMeasurementFrequencyAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Measurement Frequency [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_FairValueByMeasurementFrequencyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:to="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DueToAffiliateCurrentAndNoncurrent_9df28488-ae12-4440-9518-65e682b62898_terseLabel_en-US" xlink:label="lab_us-gaap_DueToAffiliateCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Due to affiliates</link:label>
    <link:label id="lab_us-gaap_DueToAffiliateCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_DueToAffiliateCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Due to Affiliate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DueToAffiliateCurrentAndNoncurrent" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DueToAffiliateCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DueToAffiliateCurrentAndNoncurrent" xlink:to="lab_us-gaap_DueToAffiliateCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionLineItems_8546391d-c6ff-4b74-bc59-9ebfa15aa1aa_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Related Party Transaction</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionLineItems_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Related Party Transaction [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionLineItems" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_RelatedPartyTransactionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems" xlink:to="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_country_GB_766828ac-6072-44c0-ac10-670d46ea1f29_terseLabel_en-US" xlink:label="lab_country_GB" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">United Kingdom</link:label>
    <link:label id="lab_country_GB_label_en-US" xlink:label="lab_country_GB" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">UNITED KINGDOM</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_country_GB" xlink:to="lab_country_GB" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_CommonClassSMember_5b72f233-a0f5-4cbd-9f1d-533dec4166b3_terseLabel_en-US" xlink:label="lab_hgit_CommonClassSMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Class S</link:label>
    <link:label id="lab_hgit_CommonClassSMember_label_en-US" xlink:label="lab_hgit_CommonClassSMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Class S [Member]</link:label>
    <link:label id="lab_hgit_CommonClassSMember_documentation_en-US" xlink:label="lab_hgit_CommonClassSMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Class S [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_CommonClassSMember" xlink:href="hgit-20200930.xsd#hgit_CommonClassSMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_CommonClassSMember" xlink:to="lab_hgit_CommonClassSMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_ed499d59-0c8e-492e-91e8-68e219c38cbb_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DerivativeInstrumentRiskAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:to="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionDueFromToRelatedParty_0f6a7548-3043-40fd-bc1c-ca4016aadb78_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionDueFromToRelatedParty" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Due to (from) related parties</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionDueFromToRelatedParty" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_RelatedPartyTransactionDueFromToRelatedParty"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionDueFromToRelatedParty" xlink:to="lab_us-gaap_RelatedPartyTransactionDueFromToRelatedParty" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_0eac8f1c-19e2-4f97-86de-1a7e55c500f4_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Finite-Lived Intangible Assets by Major Class [Axis]</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Finite-Lived Intangible Assets by Major Class [Axis]</link:label>
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    <link:label id="lab_us-gaap_CashFlowSupplementalDisclosuresTextBlock_1201782c-9038-4b1c-9da8-b883aeef5328_terseLabel_en-US" xlink:label="lab_us-gaap_CashFlowSupplementalDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">SUPPLEMENTAL CASH FLOW DISCLOSURES</link:label>
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    <link:label id="lab_us-gaap_DividendsDomain_01ba281b-e51b-4463-bc5b-10be35aef622_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Dividends [Domain]</link:label>
    <link:label id="lab_us-gaap_DividendsDomain_label_en-US" xlink:label="lab_us-gaap_DividendsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Dividends [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsDomain" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DividendsDomain"/>
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    <link:label id="lab_srt_StatementGeographicalAxis_a379819a-6081-49fd-9a34-3a62e34cc2bf_terseLabel_en-US" xlink:label="lab_srt_StatementGeographicalAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Geographical [Axis]</link:label>
    <link:label id="lab_srt_StatementGeographicalAxis_label_en-US" xlink:label="lab_srt_StatementGeographicalAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Geographical [Axis]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateTable" xlink:to="lab_us-gaap_RealEstateTable" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_PropertyManagementFeesMember_d5d5c4fe-79cd-4566-9f1a-1ee921c9a1f8_terseLabel_en-US" xlink:label="lab_hgit_PropertyManagementFeesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Property Management Fees</link:label>
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    <link:label id="lab_hgit_UKLogisticsMember_label_en-US" xlink:label="lab_hgit_UKLogisticsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">UK Logistics [Member]</link:label>
    <link:label id="lab_hgit_UKLogisticsMember_documentation_en-US" xlink:label="lab_hgit_UKLogisticsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">UK Logistics</link:label>
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    <link:label id="lab_hgit_MaximumProceedsFromIssuanceInitialPublicOffering_0a42a8f7-104b-4da1-a917-a36121f16d74_terseLabel_en-US" xlink:label="lab_hgit_MaximumProceedsFromIssuanceInitialPublicOffering" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Maximum proceeds from issuance of IPO</link:label>
    <link:label id="lab_hgit_MaximumProceedsFromIssuanceInitialPublicOffering_label_en-US" xlink:label="lab_hgit_MaximumProceedsFromIssuanceInitialPublicOffering" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Maximum Proceeds From Issuance Initial Public Offering</link:label>
    <link:label id="lab_hgit_MaximumProceedsFromIssuanceInitialPublicOffering_documentation_en-US" xlink:label="lab_hgit_MaximumProceedsFromIssuanceInitialPublicOffering" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Maximum proceeds available from the public offering</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_MaximumProceedsFromIssuanceInitialPublicOffering" xlink:href="hgit-20200930.xsd#hgit_MaximumProceedsFromIssuanceInitialPublicOffering"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_MaximumProceedsFromIssuanceInitialPublicOffering" xlink:to="lab_hgit_MaximumProceedsFromIssuanceInitialPublicOffering" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_684f22bd-cfcc-4c8d-9670-aec489bc8566_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_StatementOfCashFlowsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:to="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_e86797c1-8826-447e-bec3-bedb95451b8d_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">2024</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Long-Term Debt, Maturity, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BelowMarketLeaseGross_6a627e57-1307-41c9-a5e3-0ef734f9bf99_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseGross" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Out-of-Market Lease Liabilities, Cost</link:label>
    <link:label id="lab_us-gaap_BelowMarketLeaseGross_label_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Below Market Lease, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BelowMarketLeaseGross" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_BelowMarketLeaseGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BelowMarketLeaseGross" xlink:to="lab_us-gaap_BelowMarketLeaseGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_6460a888-d6f3-4926-8e25-1dd8a138c879_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Property, Plant and Equipment, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Long-Lived Tangible Asset [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_PropertyPlantAndEquipmentByTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_PercentageofPortfolioLeased_4302fcc4-34dd-4e81-883e-136d89fb38a6_terseLabel_en-US" xlink:label="lab_hgit_PercentageofPortfolioLeased" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Real estate portfolio, percentage leased</link:label>
    <link:label id="lab_hgit_PercentageofPortfolioLeased_label_en-US" xlink:label="lab_hgit_PercentageofPortfolioLeased" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Percentage of Portfolio Leased</link:label>
    <link:label id="lab_hgit_PercentageofPortfolioLeased_documentation_en-US" xlink:label="lab_hgit_PercentageofPortfolioLeased" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Percentage of Portfolio Leased</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_PercentageofPortfolioLeased" xlink:href="hgit-20200930.xsd#hgit_PercentageofPortfolioLeased"/>
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    <link:label id="lab_hgit_HinesGlobalREITIIPropertiesLPMember_852992c2-986a-453c-b0c2-c7b1a4951b33_terseLabel_en-US" xlink:label="lab_hgit_HinesGlobalREITIIPropertiesLPMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Ownership Partnership</link:label>
    <link:label id="lab_hgit_HinesGlobalREITIIPropertiesLPMember_label_en-US" xlink:label="lab_hgit_HinesGlobalREITIIPropertiesLPMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Hines Global REIT II Properties, LP [Member]</link:label>
    <link:label id="lab_hgit_HinesGlobalREITIIPropertiesLPMember_documentation_en-US" xlink:label="lab_hgit_HinesGlobalREITIIPropertiesLPMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Hines Global REIT II Properties, LP [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_HinesGlobalREITIIPropertiesLPMember" xlink:href="hgit-20200930.xsd#hgit_HinesGlobalREITIIPropertiesLPMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_HinesGlobalREITIIPropertiesLPMember" xlink:to="lab_hgit_HinesGlobalREITIIPropertiesLPMember" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_AssetManagementAndAcquisitionFees_4a3f6baf-536f-4a68-89df-0cd57314c3e3_terseLabel_en-US" xlink:label="lab_hgit_AssetManagementAndAcquisitionFees" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset management fees</link:label>
    <link:label id="lab_hgit_AssetManagementAndAcquisitionFees_label_en-US" xlink:label="lab_hgit_AssetManagementAndAcquisitionFees" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset Management And Acquisition Fees</link:label>
    <link:label id="lab_hgit_AssetManagementAndAcquisitionFees_documentation_en-US" xlink:label="lab_hgit_AssetManagementAndAcquisitionFees" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset management and acquisition fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_AssetManagementAndAcquisitionFees" xlink:href="hgit-20200930.xsd#hgit_AssetManagementAndAcquisitionFees"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_AssetManagementAndAcquisitionFees" xlink:to="lab_hgit_AssetManagementAndAcquisitionFees" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationReclassificationAdjustmentFromAOCIRealizedUponSaleOrLiquidationNetOfTax_37409ea2-576c-421a-b66a-f8b0b2719fb2_negatedLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationReclassificationAdjustmentFromAOCIRealizedUponSaleOrLiquidationNetOfTax" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Foreign currency translation adjustment reclassified into earnings</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationReclassificationAdjustmentFromAOCIRealizedUponSaleOrLiquidationNetOfTax_d709c863-7580-4adf-859f-85aa9667b2d9_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationReclassificationAdjustmentFromAOCIRealizedUponSaleOrLiquidationNetOfTax" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Realized loss related to currency translation adjustment</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationReclassificationAdjustmentFromAOCIRealizedUponSaleOrLiquidationNetOfTax" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationReclassificationAdjustmentFromAOCIRealizedUponSaleOrLiquidationNetOfTax"/>
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    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_203a8ddd-ebc5-49ab-bd75-a74cfe51ee8b_terseLabel_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_label_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
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    <link:label id="lab_hgit_DeferredFinancingCostsNetPermanentMortgages_363ee9e6-81b5-46b9-ac40-2f3231e20c7e_negatedTerseLabel_en-US" xlink:label="lab_hgit_DeferredFinancingCostsNetPermanentMortgages" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Unamortized financing fees</link:label>
    <link:label id="lab_hgit_DeferredFinancingCostsNetPermanentMortgages_label_en-US" xlink:label="lab_hgit_DeferredFinancingCostsNetPermanentMortgages" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Deferred Financing Costs, Net, Permanent Mortgages</link:label>
    <link:label id="lab_hgit_DeferredFinancingCostsNetPermanentMortgages_documentation_en-US" xlink:label="lab_hgit_DeferredFinancingCostsNetPermanentMortgages" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Deferred Financing Costs, Net, Permanent Mortgages</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_DeferredFinancingCostsNetPermanentMortgages" xlink:href="hgit-20200930.xsd#hgit_DeferredFinancingCostsNetPermanentMortgages"/>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_741ca3b8-6785-4c0e-a54d-1f49e2bd48d5_verboseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">CASH FLOWS FROM FINANCING ACTIVITIES:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net Cash Provided by (Used in) Financing Activities [Abstract]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReceivablesPolicyTextBlock_a6b962da-cfdd-4d57-9f5b-b8110ab00302_terseLabel_en-US" xlink:label="lab_us-gaap_ReceivablesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Tenant and Other Receivables</link:label>
    <link:label id="lab_us-gaap_ReceivablesPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ReceivablesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Receivable [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReceivablesPolicyTextBlock" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ReceivablesPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReceivablesPolicyTextBlock" xlink:to="lab_us-gaap_ReceivablesPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_RedemptionsPayable_b1e6486d-2ecf-4320-b806-748d8d289b2a_terseLabel_en-US" xlink:label="lab_hgit_RedemptionsPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Shares tendered for redemption</link:label>
    <link:label id="lab_hgit_RedemptionsPayable_label_en-US" xlink:label="lab_hgit_RedemptionsPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Redemptions Payable</link:label>
    <link:label id="lab_hgit_RedemptionsPayable_documentation_en-US" xlink:label="lab_hgit_RedemptionsPayable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">The future cash outflow to pay for redemptions of common stock.</link:label>
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    <link:label id="lab_us-gaap_DerivativeNotionalAmount_5f70b48a-713c-49ba-afaa-764d0042e141_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative, notional amount</link:label>
    <link:label id="lab_us-gaap_DerivativeNotionalAmount_label_en-US" xlink:label="lab_us-gaap_DerivativeNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative, Notional Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeNotionalAmount" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DerivativeNotionalAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeNotionalAmount" xlink:to="lab_us-gaap_DerivativeNotionalAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfIntangibleAssets_e31c1ea0-54ba-4035-86cb-6db19f165d3b_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Amortization of in-place leases</link:label>
    <link:label id="lab_us-gaap_AmortizationOfIntangibleAssets_label_en-US" xlink:label="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Amortization of Intangible Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfIntangibleAssets" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_AmortizationOfIntangibleAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfIntangibleAssets" xlink:to="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_BishopsSquareMember_1ad031f6-5e96-4047-a0b6-96dc296149aa_terseLabel_en-US" xlink:label="lab_hgit_BishopsSquareMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Bishop's Square</link:label>
    <link:label id="lab_hgit_BishopsSquareMember_label_en-US" xlink:label="lab_hgit_BishopsSquareMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Bishop's Square [Member]</link:label>
    <link:label id="lab_hgit_BishopsSquareMember_documentation_en-US" xlink:label="lab_hgit_BishopsSquareMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Bishop's Square</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_BishopsSquareMember" xlink:href="hgit-20200930.xsd#hgit_BishopsSquareMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_BishopsSquareMember" xlink:to="lab_hgit_BishopsSquareMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPMembersOrLimitedPartnersOwnershipInterest_be26d9d3-0004-4294-a096-1cb70cfbaeb1_terseLabel_en-US" xlink:label="lab_us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPMembersOrLimitedPartnersOwnershipInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Ownership interest percentage (less than)</link:label>
    <link:label id="lab_us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPMembersOrLimitedPartnersOwnershipInterest_label_en-US" xlink:label="lab_us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPMembersOrLimitedPartnersOwnershipInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Limited Liability Company or Limited Partnership, Members or Limited Partners, Ownership Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPMembersOrLimitedPartnersOwnershipInterest" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPMembersOrLimitedPartnersOwnershipInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPMembersOrLimitedPartnersOwnershipInterest" xlink:to="lab_us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPMembersOrLimitedPartnersOwnershipInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PrepaidTaxes_9cf76272-acb2-44ad-92ff-9e1d7971c075_terseLabel_en-US" xlink:label="lab_us-gaap_PrepaidTaxes" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Prepaid property taxes</link:label>
    <link:label id="lab_us-gaap_PrepaidTaxes_label_en-US" xlink:label="lab_us-gaap_PrepaidTaxes" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Prepaid Taxes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepaidTaxes" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_PrepaidTaxes"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PrepaidTaxes" xlink:to="lab_us-gaap_PrepaidTaxes" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_FiniteLivedIntangibleLiabilitiesAcquired_142334f9-ba5d-4afc-8298-135ab5ce9e91_negatedTerseLabel_en-US" xlink:label="lab_hgit_FiniteLivedIntangibleLiabilitiesAcquired" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Out-of-market lease intangibles, net</link:label>
    <link:label id="lab_hgit_FiniteLivedIntangibleLiabilitiesAcquired_label_en-US" xlink:label="lab_hgit_FiniteLivedIntangibleLiabilitiesAcquired" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Finite-Lived Intangible Liabilities Acquired</link:label>
    <link:label id="lab_hgit_FiniteLivedIntangibleLiabilitiesAcquired_documentation_en-US" xlink:label="lab_hgit_FiniteLivedIntangibleLiabilitiesAcquired" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Finite-Lived Intangible Liabilities Acquired</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_FiniteLivedIntangibleLiabilitiesAcquired" xlink:href="hgit-20200930.xsd#hgit_FiniteLivedIntangibleLiabilitiesAcquired"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_FiniteLivedIntangibleLiabilitiesAcquired" xlink:to="lab_hgit_FiniteLivedIntangibleLiabilitiesAcquired" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_HinesGlobalREITIIAssociatesLPMember_7f0ed88e-f69c-45de-8b2c-51c3bf28b792_terseLabel_en-US" xlink:label="lab_hgit_HinesGlobalREITIIAssociatesLPMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Hines Global REIT II Associates LP</link:label>
    <link:label id="lab_hgit_HinesGlobalREITIIAssociatesLPMember_label_en-US" xlink:label="lab_hgit_HinesGlobalREITIIAssociatesLPMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Hines Global REIT II Associates LP [Member]</link:label>
    <link:label id="lab_hgit_HinesGlobalREITIIAssociatesLPMember_documentation_en-US" xlink:label="lab_hgit_HinesGlobalREITIIAssociatesLPMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Hines Global REIT II Associates LP [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_HinesGlobalREITIIAssociatesLPMember" xlink:href="hgit-20200930.xsd#hgit_HinesGlobalREITIIAssociatesLPMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_HinesGlobalREITIIAssociatesLPMember" xlink:to="lab_hgit_HinesGlobalREITIIAssociatesLPMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAverageVariableInterestRate_36c78434-fe76-497a-981d-f854dc1b1090_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAverageVariableInterestRate" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative, swap pay rate/strike rate (percent)</link:label>
    <link:label id="lab_us-gaap_DerivativeAverageVariableInterestRate_label_en-US" xlink:label="lab_us-gaap_DerivativeAverageVariableInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative, Average Variable Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAverageVariableInterestRate" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DerivativeAverageVariableInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAverageVariableInterestRate" xlink:to="lab_us-gaap_DerivativeAverageVariableInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_Percentageofrentcollected_90ff8cb9-2599-4251-a0bd-5a38a96c34e5_terseLabel_en-US" xlink:label="lab_hgit_Percentageofrentcollected" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Percentage of rent collected</link:label>
    <link:label id="lab_hgit_Percentageofrentcollected_label_en-US" xlink:label="lab_hgit_Percentageofrentcollected" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Percentage of rent collected</link:label>
    <link:label id="lab_hgit_Percentageofrentcollected_documentation_en-US" xlink:label="lab_hgit_Percentageofrentcollected" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Percentage of rent collected</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_Percentageofrentcollected" xlink:href="hgit-20200930.xsd#hgit_Percentageofrentcollected"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_Percentageofrentcollected" xlink:to="lab_hgit_Percentageofrentcollected" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BelowMarketLeaseNet_0580e71b-5104-4c4a-94ae-e9fd91a4f8bb_negatedTotalLabel_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseNet" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Out-of-Market Lease Liabilities, Net</link:label>
    <link:label id="lab_us-gaap_BelowMarketLeaseNet_label_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Below Market Lease, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BelowMarketLeaseNet" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_BelowMarketLeaseNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BelowMarketLeaseNet" xlink:to="lab_us-gaap_BelowMarketLeaseNet" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_PublicOfferingAxis_999682df-a80e-4cd4-b842-dfe17b3ee258_terseLabel_en-US" xlink:label="lab_hgit_PublicOfferingAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Public Offering [Axis]</link:label>
    <link:label id="lab_hgit_PublicOfferingAxis_label_en-US" xlink:label="lab_hgit_PublicOfferingAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Public Offering [Axis]</link:label>
    <link:label id="lab_hgit_PublicOfferingAxis_documentation_en-US" xlink:label="lab_hgit_PublicOfferingAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Public Offering [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_PublicOfferingAxis" xlink:href="hgit-20200930.xsd#hgit_PublicOfferingAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_PublicOfferingAxis" xlink:to="lab_hgit_PublicOfferingAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilities_92604410-25a3-4ca6-9712-33a325da2f75_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilities_label_en-US" xlink:label="lab_us-gaap_OtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilities" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_OtherLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilities" xlink:to="lab_us-gaap_OtherLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingDisclosureTextBlock_4afc5d94-afcb-415d-8efe-8e5ae229feb1_verboseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">REPORTABLE SEGMENTS</link:label>
    <link:label id="lab_us-gaap_SegmentReportingDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Segment Reporting Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_SegmentReportingDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:to="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_34c01738-b9b7-4f82-97a1-dbec2e1d24af_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Issuance of common shares, value</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Stock Issued During Period, Value, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_StockIssuedDuringPeriodValueNewIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BelowMarketLeaseNetAmortizationIncomeFiscalYearMaturityAbstract_c62b75fe-cd93-46e5-8ad8-ff0d1dd145e0_terseLabel_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseNetAmortizationIncomeFiscalYearMaturityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Out-of-Market Leases, Net</link:label>
    <link:label id="lab_us-gaap_BelowMarketLeaseNetAmortizationIncomeFiscalYearMaturityAbstract_label_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseNetAmortizationIncomeFiscalYearMaturityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Below Market Lease, Net, Amortization Income, Fiscal Year Maturity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BelowMarketLeaseNetAmortizationIncomeFiscalYearMaturityAbstract" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_BelowMarketLeaseNetAmortizationIncomeFiscalYearMaturityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BelowMarketLeaseNetAmortizationIncomeFiscalYearMaturityAbstract" xlink:to="lab_us-gaap_BelowMarketLeaseNetAmortizationIncomeFiscalYearMaturityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Assets_933d90e6-ad27-4e40-aef3-00b404cb266d_totalLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_us-gaap_Assets_ea36a9a4-aab6-4940-a3c4-43c93b87dae6_terseLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_us-gaap_Assets_label_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_Assets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Assets" xlink:to="lab_us-gaap_Assets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_369f06a5-a40e-411c-947d-6a7a03a9ad5a_verboseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">RELATED PARTY TRANSACTIONS</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Related Party Transactions Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_RelatedPartyTransactionsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:to="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_VenueMuseumDistrictMember_4bff7074-8a3e-4575-8ef6-1045f2e82fb1_terseLabel_en-US" xlink:label="lab_hgit_VenueMuseumDistrictMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Venue Museum District</link:label>
    <link:label id="lab_hgit_VenueMuseumDistrictMember_label_en-US" xlink:label="lab_hgit_VenueMuseumDistrictMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Venue Museum District [Member]</link:label>
    <link:label id="lab_hgit_VenueMuseumDistrictMember_documentation_en-US" xlink:label="lab_hgit_VenueMuseumDistrictMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Venue Museum District [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_VenueMuseumDistrictMember" xlink:href="hgit-20200930.xsd#hgit_VenueMuseumDistrictMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_VenueMuseumDistrictMember" xlink:to="lab_hgit_VenueMuseumDistrictMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseDebt_5110b352-ab5b-4f83-8400-be457261d0cf_negatedLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseDebt" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseDebt_4440ba52-ed87-4d34-851e-9e2ba72f96ee_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseDebt_label_en-US" xlink:label="lab_us-gaap_InterestExpenseDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Interest Expense, Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseDebt" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_InterestExpenseDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseDebt" xlink:to="lab_us-gaap_InterestExpenseDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupClassificationAxis_f453948c-6fd0-459d-90ba-6f1f9e838082_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupClassificationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Disposal Group Classification [Axis]</link:label>
    <link:label id="lab_us-gaap_DisposalGroupClassificationAxis_label_en-US" xlink:label="lab_us-gaap_DisposalGroupClassificationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Disposal Group Classification [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupClassificationAxis" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DisposalGroupClassificationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupClassificationAxis" xlink:to="lab_us-gaap_DisposalGroupClassificationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_d786e527-b5a4-45db-a892-90bdf2d5b1bc_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Intangible lease assets, net</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_10a02d5e-88b5-47c0-b490-ab8c533cc4ee_totalLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Finite-Lived Intangible Assets, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_FiniteLivedIntangibleAssetsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_DeferredRentAllowanceForCreditLossDueToRentReliefProvidedToTenantByDeferral_b534a0f7-e47f-4d9b-b254-8ffc16e601fe_terseLabel_en-US" xlink:label="lab_hgit_DeferredRentAllowanceForCreditLossDueToRentReliefProvidedToTenantByDeferral" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Deferred rent, allowance for credit loss due to rent relief provided to tenant by deferral</link:label>
    <link:label id="lab_hgit_DeferredRentAllowanceForCreditLossDueToRentReliefProvidedToTenantByDeferral_label_en-US" xlink:label="lab_hgit_DeferredRentAllowanceForCreditLossDueToRentReliefProvidedToTenantByDeferral" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Deferred rent, allowance for credit loss due to rent relief provided to tenant by deferral</link:label>
    <link:label id="lab_hgit_DeferredRentAllowanceForCreditLossDueToRentReliefProvidedToTenantByDeferral_documentation_en-US" xlink:label="lab_hgit_DeferredRentAllowanceForCreditLossDueToRentReliefProvidedToTenantByDeferral" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Deferred rent, allowance for credit loss due to rent relief provided to tenant by deferral</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_DeferredRentAllowanceForCreditLossDueToRentReliefProvidedToTenantByDeferral" xlink:href="hgit-20200930.xsd#hgit_DeferredRentAllowanceForCreditLossDueToRentReliefProvidedToTenantByDeferral"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_DeferredRentAllowanceForCreditLossDueToRentReliefProvidedToTenantByDeferral" xlink:to="lab_hgit_DeferredRentAllowanceForCreditLossDueToRentReliefProvidedToTenantByDeferral" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingDisclosureOfEntitysReportableSegmentsAbstract_3d780941-0784-43e1-8a6b-e41ca925ae07_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureOfEntitysReportableSegmentsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Segment Reporting, Disclosure of Entity's Reportable Segments</link:label>
    <link:label id="lab_us-gaap_SegmentReportingDisclosureOfEntitysReportableSegmentsAbstract_label_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureOfEntitysReportableSegmentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Segment Reporting, Disclosure of Entity's Reportable Segments [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingDisclosureOfEntitysReportableSegmentsAbstract" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_SegmentReportingDisclosureOfEntitysReportableSegmentsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingDisclosureOfEntitysReportableSegmentsAbstract" xlink:to="lab_us-gaap_SegmentReportingDisclosureOfEntitysReportableSegmentsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_f88d8ad0-91b6-4e78-b32d-fb93240a2aeb_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeAxis" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_SubsequentEventTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeAxis" xlink:to="lab_us-gaap_SubsequentEventTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfCommonStockOutstandingRollForwardTableTextBlock_a431e93f-8446-4af8-9089-d6963aa563ea_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfCommonStockOutstandingRollForwardTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Common Stock Outstanding Roll Forward</link:label>
    <link:label id="lab_us-gaap_ScheduleOfCommonStockOutstandingRollForwardTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfCommonStockOutstandingRollForwardTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Common Stock Outstanding Roll Forward [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfCommonStockOutstandingRollForwardTableTextBlock" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ScheduleOfCommonStockOutstandingRollForwardTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfCommonStockOutstandingRollForwardTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfCommonStockOutstandingRollForwardTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_Contract1Member_6a4e8c89-a5dd-404f-89e9-e3fb4f07e15b_terseLabel_en-US" xlink:label="lab_hgit_Contract1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Foreign exchange forward contract</link:label>
    <link:label id="lab_hgit_Contract1Member_label_en-US" xlink:label="lab_hgit_Contract1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract 1 [Member]</link:label>
    <link:label id="lab_hgit_Contract1Member_documentation_en-US" xlink:label="lab_hgit_Contract1Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract 1 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_Contract1Member" xlink:href="hgit-20200930.xsd#hgit_Contract1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_Contract1Member" xlink:to="lab_hgit_Contract1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears_6aae74db-eda6-4888-89ee-5e04f027f949_terseLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">2022</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DirectOperatingCosts_1e2d9e96-6332-4acf-9772-141c79bbc0ef_terseLabel_en-US" xlink:label="lab_us-gaap_DirectOperatingCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Property operating expenses</link:label>
    <link:label id="lab_us-gaap_DirectOperatingCosts_label_en-US" xlink:label="lab_us-gaap_DirectOperatingCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Direct Operating Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DirectOperatingCosts" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DirectOperatingCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DirectOperatingCosts" xlink:to="lab_us-gaap_DirectOperatingCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_CommonClassIXMember_48d68318-fefe-4bb9-8b29-3dbce95d55cb_terseLabel_en-US" xlink:label="lab_hgit_CommonClassIXMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Class IX</link:label>
    <link:label id="lab_hgit_CommonClassIXMember_label_en-US" xlink:label="lab_hgit_CommonClassIXMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Class IX [Member]</link:label>
    <link:label id="lab_hgit_CommonClassIXMember_documentation_en-US" xlink:label="lab_hgit_CommonClassIXMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Class IX [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_CommonClassIXMember" xlink:href="hgit-20200930.xsd#hgit_CommonClassIXMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_CommonClassIXMember" xlink:to="lab_hgit_CommonClassIXMember" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_FreshParkVenloMember_f9f03467-cd58-4633-8d22-2a6b504290d7_terseLabel_en-US" xlink:label="lab_hgit_FreshParkVenloMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fresh Park Venlo</link:label>
    <link:label id="lab_hgit_FreshParkVenloMember_label_en-US" xlink:label="lab_hgit_FreshParkVenloMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fresh Park Venlo [Member]</link:label>
    <link:label id="lab_hgit_FreshParkVenloMember_documentation_en-US" xlink:label="lab_hgit_FreshParkVenloMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fresh Park Venlo [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_FreshParkVenloMember" xlink:href="hgit-20200930.xsd#hgit_FreshParkVenloMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_FreshParkVenloMember" xlink:to="lab_hgit_FreshParkVenloMember" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_DisposalGroupIncludingDiscontinuedOperationInvestmentProperty_c9a3b32c-026f-4dde-a3ce-6fd23c0486c7_terseLabel_en-US" xlink:label="lab_hgit_DisposalGroupIncludingDiscontinuedOperationInvestmentProperty" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Investments in property, net classified with assets held for sale</link:label>
    <link:label id="lab_hgit_DisposalGroupIncludingDiscontinuedOperationInvestmentProperty_label_en-US" xlink:label="lab_hgit_DisposalGroupIncludingDiscontinuedOperationInvestmentProperty" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Investment Property</link:label>
    <link:label id="lab_hgit_DisposalGroupIncludingDiscontinuedOperationInvestmentProperty_documentation_en-US" xlink:label="lab_hgit_DisposalGroupIncludingDiscontinuedOperationInvestmentProperty" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Investment Property</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_DisposalGroupIncludingDiscontinuedOperationInvestmentProperty" xlink:href="hgit-20200930.xsd#hgit_DisposalGroupIncludingDiscontinuedOperationInvestmentProperty"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_DisposalGroupIncludingDiscontinuedOperationInvestmentProperty" xlink:to="lab_hgit_DisposalGroupIncludingDiscontinuedOperationInvestmentProperty" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ProductOrServiceAxis_bca53f2b-ae13-4847-a66d-ffe228dd4e1f_terseLabel_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:label id="lab_srt_ProductOrServiceAxis_label_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductOrServiceAxis" xlink:href="http://xbrl.fasb.org/srt/2020/elts/srt-2020-01-31.xsd#srt_ProductOrServiceAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProductOrServiceAxis" xlink:to="lab_srt_ProductOrServiceAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Liabilities_e37a2969-9a64-49c8-80b4-84a1ce46c758_totalLabel_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total liabilities</link:label>
    <link:label id="lab_us-gaap_Liabilities_label_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Liabilities" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_Liabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Liabilities" xlink:to="lab_us-gaap_Liabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SalesMember_21420088-1068-40b9-9d14-5923cf86d2a8_terseLabel_en-US" xlink:label="lab_us-gaap_SalesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total Revenue</link:label>
    <link:label id="lab_us-gaap_SalesMember_label_en-US" xlink:label="lab_us-gaap_SalesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Sales [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SalesMember" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_SalesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SalesMember" xlink:to="lab_us-gaap_SalesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_DomesticRetailRealEstateInvestmentsMember_1dde8c02-fd9d-4a0b-812b-2e44cc692106_terseLabel_en-US" xlink:label="lab_hgit_DomesticRetailRealEstateInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Domestic retail investments</link:label>
    <link:label id="lab_hgit_DomesticRetailRealEstateInvestmentsMember_label_en-US" xlink:label="lab_hgit_DomesticRetailRealEstateInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Domestic Retail Real Estate Investments [Member]</link:label>
    <link:label id="lab_hgit_DomesticRetailRealEstateInvestmentsMember_documentation_en-US" xlink:label="lab_hgit_DomesticRetailRealEstateInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Domestic Retail Real Estate Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_DomesticRetailRealEstateInvestmentsMember" xlink:href="hgit-20200930.xsd#hgit_DomesticRetailRealEstateInvestmentsMember"/>
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    <link:label id="lab_us-gaap_RealEstateAbstract_9578f4f0-8b4e-403b-91a3-77caa2a07a21_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Real Estate [Abstract]</link:label>
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    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_99b0c7c2-f761-4ad1-b5be-f4c6b68bbfd3_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Hines Global Income Trust, Inc. Additional Paid-in Capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Additional Paid-in Capital [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_AdditionalPaidInCapitalMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:to="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAssets_3331f75b-5a8b-4258-81d1-f7c734ee2464_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_OtherAssets_c45be224-955c-4a2c-9a4a-e59d6758b6a3_totalLabel_en-US" xlink:label="lab_us-gaap_OtherAssets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_OtherAssets_label_en-US" xlink:label="lab_us-gaap_OtherAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssets" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_OtherAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssets" xlink:to="lab_us-gaap_OtherAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingSegmentsMember_a09dfdcf-a8ec-4055-97f5-c90967b28ebc_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingSegmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Operating Segments</link:label>
    <link:label id="lab_us-gaap_OperatingSegmentsMember_label_en-US" xlink:label="lab_us-gaap_OperatingSegmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Operating Segments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingSegmentsMember" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_OperatingSegmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingSegmentsMember" xlink:to="lab_us-gaap_OperatingSegmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedDistributionsInExcessOfNetIncomeMember_23b2b18d-3115-4a3f-bfa3-5bd1c5593caa_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedDistributionsInExcessOfNetIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accumulated Distributions in Excess of Earnings</link:label>
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    <link:label id="lab_us-gaap_AssetsMember_2358bed5-c176-4cdc-aa0f-21e2ca2ff382_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total Assets</link:label>
    <link:label id="lab_us-gaap_AssetsMember_label_en-US" xlink:label="lab_us-gaap_AssetsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Assets [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsMember" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_AssetsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsMember" xlink:to="lab_us-gaap_AssetsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_PaymentsReceivedFromRelatedParties_b033ecd4-bc4d-41a9-b2c3-bf432c87be5c_terseLabel_en-US" xlink:label="lab_hgit_PaymentsReceivedFromRelatedParties" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments received from related parties</link:label>
    <link:label id="lab_hgit_PaymentsReceivedFromRelatedParties_label_en-US" xlink:label="lab_hgit_PaymentsReceivedFromRelatedParties" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments Received From Related Parties</link:label>
    <link:label id="lab_hgit_PaymentsReceivedFromRelatedParties_documentation_en-US" xlink:label="lab_hgit_PaymentsReceivedFromRelatedParties" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments Received From Related Parties</link:label>
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    <link:label id="lab_us-gaap_ClassOfStockLineItems_f15a8d6d-f9fe-4463-a727-ba8cba84f1fe_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Stock [Line Items]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockLineItems_label_en-US" xlink:label="lab_us-gaap_ClassOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Stock [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockLineItems" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ClassOfStockLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfStockLineItems" xlink:to="lab_us-gaap_ClassOfStockLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_9a4821c3-0db4-459e-879a-0ab17484114a_verboseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Adjustments to reconcile net income (loss) to net cash from (used in) operating activities:</link:label>
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    <link:label id="lab_us-gaap_GainsLossesOnSalesOfInvestmentRealEstate_8b0ae804-2b3e-465b-9265-9c6df6f3ec52_terseLabel_en-US" xlink:label="lab_us-gaap_GainsLossesOnSalesOfInvestmentRealEstate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Gain on sale of real estate</link:label>
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    <link:label id="lab_us-gaap_GainsLossesOnSalesOfInvestmentRealEstate_ca1db501-5b96-4fd1-8c22-00c006df8257_verboseLabel_en-US" xlink:label="lab_us-gaap_GainsLossesOnSalesOfInvestmentRealEstate" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Gains (loss) on sale of real estate</link:label>
    <link:label id="lab_us-gaap_GainsLossesOnSalesOfInvestmentRealEstate_label_en-US" xlink:label="lab_us-gaap_GainsLossesOnSalesOfInvestmentRealEstate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Gains (Losses) on Sales of Investment Real Estate</link:label>
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    <link:label id="lab_us-gaap_DerivativeLiabilities_98bedc5f-6ded-44d8-bd79-82fbd42faa1a_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative instruments</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilities_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Liability</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilities" xlink:to="lab_us-gaap_DerivativeLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_PropertyRevenuesInExcessOfExpenses_f94bb7b4-ba31-430d-8e1d-a788101df225_terseLabel_en-US" xlink:label="lab_hgit_PropertyRevenuesInExcessOfExpenses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total revenues in excess of property expenses</link:label>
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    <link:label id="lab_hgit_PropertyRevenuesInExcessOfExpenses_documentation_en-US" xlink:label="lab_hgit_PropertyRevenuesInExcessOfExpenses" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenues less property operating expenses, real property taxes and property management fees.</link:label>
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    <link:label id="lab_hgit_CottonwoodCorporateCenterMember_5be0e57d-979b-4327-93bb-a9dadf9afd15_terseLabel_en-US" xlink:label="lab_hgit_CottonwoodCorporateCenterMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cottonwood Corporate Center</link:label>
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    <link:label id="lab_us-gaap_OtherReceivables_aad9e135-710f-4b4e-b447-10439c97ca5b_terseLabel_en-US" xlink:label="lab_us-gaap_OtherReceivables" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Receivable related to sale included in tenant and other receivables</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherReceivables" xlink:to="lab_us-gaap_OtherReceivables" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy_002f8593-5ae6-405b-8d6d-ed2b13d7bf37_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value Measurements</link:label>
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    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_7850957b-c54c-493d-8696-35db6e6d1ae6_periodStartLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Beginning balance, shares (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_fcc1c253-befa-40a1-b807-ab0264226f93_periodEndLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Ending balance, shares (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_cc6c9f89-de8d-4113-8bcf-aa123b3241a0_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common stock, shares outstanding (in shares)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesOutstanding" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_CommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesOutstanding" xlink:to="lab_us-gaap_CommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityInformationLineItems_3c1e145b-4364-44ce-9e01-5be52b7f0373_terseLabel_en-US" xlink:label="lab_dei_EntityInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Information</link:label>
    <link:label id="lab_dei_EntityInformationLineItems_label_en-US" xlink:label="lab_dei_EntityInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityInformationLineItems" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_EntityInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInformationLineItems" xlink:to="lab_dei_EntityInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingCostsAndExpensesAbstract_00beef03-db95-475b-8330-cde93a11734c_verboseLabel_en-US" xlink:label="lab_us-gaap_OperatingCostsAndExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Expenses:</link:label>
    <link:label id="lab_us-gaap_OperatingCostsAndExpensesAbstract_label_en-US" xlink:label="lab_us-gaap_OperatingCostsAndExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Operating Costs and Expenses [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingCostsAndExpensesAbstract" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_OperatingCostsAndExpensesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingCostsAndExpensesAbstract" xlink:to="lab_us-gaap_OperatingCostsAndExpensesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevolvingCreditFacilityMember_9911fc20-4924-4033-a0f5-7f81d85f5fd8_terseLabel_en-US" xlink:label="lab_us-gaap_RevolvingCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revolving Credit Facility</link:label>
    <link:label id="lab_us-gaap_RevolvingCreditFacilityMember_label_en-US" xlink:label="lab_us-gaap_RevolvingCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revolving Credit Facility [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevolvingCreditFacilityMember" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_RevolvingCreditFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevolvingCreditFacilityMember" xlink:to="lab_us-gaap_RevolvingCreditFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BelowMarketLeaseAmortizationIncomeYearFive_5d3a258f-c778-4732-91c3-5e39fc6665cb_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseAmortizationIncomeYearFive" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">2025</link:label>
    <link:label id="lab_us-gaap_BelowMarketLeaseAmortizationIncomeYearFive_label_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseAmortizationIncomeYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Below Market Lease, Amortization Income, Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BelowMarketLeaseAmortizationIncomeYearFive" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_BelowMarketLeaseAmortizationIncomeYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BelowMarketLeaseAmortizationIncomeYearFive" xlink:to="lab_us-gaap_BelowMarketLeaseAmortizationIncomeYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_CommonStockDividendsPerSharePerMonthDeclared_11af163e-cd56-4415-aae1-0639531dd57a_terseLabel_en-US" xlink:label="lab_hgit_CommonStockDividendsPerSharePerMonthDeclared" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Distribution rate per share, per month</link:label>
    <link:label id="lab_hgit_CommonStockDividendsPerSharePerMonthDeclared_label_en-US" xlink:label="lab_hgit_CommonStockDividendsPerSharePerMonthDeclared" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Stock Dividends Per Share Per Month Declared</link:label>
    <link:label id="lab_hgit_CommonStockDividendsPerSharePerMonthDeclared_documentation_en-US" xlink:label="lab_hgit_CommonStockDividendsPerSharePerMonthDeclared" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Stock Dividends Per Share Per Month Declared</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_CommonStockDividendsPerSharePerMonthDeclared" xlink:href="hgit-20200930.xsd#hgit_CommonStockDividendsPerSharePerMonthDeclared"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_CommonStockDividendsPerSharePerMonthDeclared" xlink:to="lab_hgit_CommonStockDividendsPerSharePerMonthDeclared" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_AssetManagementFeeMember_64129d92-0cd1-4b57-8e35-18de78e5d7fb_terseLabel_en-US" xlink:label="lab_hgit_AssetManagementFeeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset Management Fee</link:label>
    <link:label id="lab_hgit_AssetManagementFeeMember_label_en-US" xlink:label="lab_hgit_AssetManagementFeeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset Management Fee [Member]</link:label>
    <link:label id="lab_hgit_AssetManagementFeeMember_documentation_en-US" xlink:label="lab_hgit_AssetManagementFeeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">The fee which is equal to a percentage per month of the cost of the Company's real estate investments as of the end of each month. If the Company has determined an estimated net asset value per share, then, with respect to real estate investments included in the board of director's determination, the asset management fees will be calculated using the determined values of such real estate investments at the end of each month.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_AssetManagementFeeMember" xlink:href="hgit-20200930.xsd#hgit_AssetManagementFeeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_AssetManagementFeeMember" xlink:to="lab_hgit_AssetManagementFeeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IPOMember_6f2b5a57-786d-472e-84a0-a5570d586b29_terseLabel_en-US" xlink:label="lab_us-gaap_IPOMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Initial Offering</link:label>
    <link:label id="lab_us-gaap_IPOMember_label_en-US" xlink:label="lab_us-gaap_IPOMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">IPO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IPOMember" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_IPOMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IPOMember" xlink:to="lab_us-gaap_IPOMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedDistributionsInExcessOfNetIncome_3b17f97d-dadb-4926-8902-1dcdbbbf089f_negatedLabel_en-US" xlink:label="lab_us-gaap_AccumulatedDistributionsInExcessOfNetIncome" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accumulated distributions in excess of earnings</link:label>
    <link:label id="lab_us-gaap_AccumulatedDistributionsInExcessOfNetIncome_label_en-US" xlink:label="lab_us-gaap_AccumulatedDistributionsInExcessOfNetIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accumulated Distributions in Excess of Net Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedDistributionsInExcessOfNetIncome" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_AccumulatedDistributionsInExcessOfNetIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedDistributionsInExcessOfNetIncome" xlink:to="lab_us-gaap_AccumulatedDistributionsInExcessOfNetIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_country_PL_8bad1566-5def-4345-9fa3-6d450437d5f4_terseLabel_en-US" xlink:label="lab_country_PL" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Poland</link:label>
    <link:label id="lab_country_PL_label_en-US" xlink:label="lab_country_PL" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">POLAND</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_country_PL" xlink:href="https://xbrl.sec.gov/country/2020/country-2020-01-31.xsd#country_PL"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_country_PL" xlink:to="lab_country_PL" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventMember_4457d789-fb7e-4323-bba1-e7965823c26e_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Subsequent Event</link:label>
    <link:label id="lab_us-gaap_SubsequentEventMember_label_en-US" xlink:label="lab_us-gaap_SubsequentEventMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Subsequent Event [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventMember" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_SubsequentEventMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventMember" xlink:to="lab_us-gaap_SubsequentEventMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NotesPayableToBanksMember_c775d03f-5033-4728-a3ac-eb319d7b19a3_terseLabel_en-US" xlink:label="lab_us-gaap_NotesPayableToBanksMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Term Loan Facility</link:label>
    <link:label id="lab_us-gaap_NotesPayableToBanksMember_label_en-US" xlink:label="lab_us-gaap_NotesPayableToBanksMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Notes Payable to Banks [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NotesPayableToBanksMember" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_NotesPayableToBanksMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NotesPayableToBanksMember" xlink:to="lab_us-gaap_NotesPayableToBanksMember" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_OutOfMarketLeasesNetMember_8e6a6f32-84bf-4454-882f-0b825c190c62_terseLabel_en-US" xlink:label="lab_hgit_OutOfMarketLeasesNetMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Out-of-Market Leases, Net</link:label>
    <link:label id="lab_hgit_OutOfMarketLeasesNetMember_label_en-US" xlink:label="lab_hgit_OutOfMarketLeasesNetMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Out Of Market Leases Net [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_OutOfMarketLeasesNetMember" xlink:href="hgit-20200930.xsd#hgit_OutOfMarketLeasesNetMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_OutOfMarketLeasesNetMember" xlink:to="lab_hgit_OutOfMarketLeasesNetMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_e426a8fb-e323-4aa0-9223-4476090e35ca_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common stock, shares authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesAuthorized" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_CommonStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesAuthorized" xlink:to="lab_us-gaap_CommonStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_3d79edf8-f290-4b6f-8736-40f1bde737c5_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Segment Reporting Information, by Segment</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Segment Reporting Information, by Segment [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:to="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_DealerManagerFeeMember_53b93181-8e13-4cee-93ff-0dce2124c620_terseLabel_en-US" xlink:label="lab_hgit_DealerManagerFeeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Dealer Manager Fee</link:label>
    <link:label id="lab_hgit_DealerManagerFeeMember_label_en-US" xlink:label="lab_hgit_DealerManagerFeeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Dealer Manager Fee [Member]</link:label>
    <link:label id="lab_hgit_DealerManagerFeeMember_documentation_en-US" xlink:label="lab_hgit_DealerManagerFeeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">The dealer manager fee based on gross offering proceeds.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_DealerManagerFeeMember" xlink:href="hgit-20200930.xsd#hgit_DealerManagerFeeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_DealerManagerFeeMember" xlink:to="lab_hgit_DealerManagerFeeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock_59da8661-dbcd-45a9-aa45-79654df42f6c_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Real Estate Properties</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Real Estate Properties [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementAbstract_94b6cc3c-6241-4eb5-b14d-c30e273d3054_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income Statement [Abstract]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income Statement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementAbstract" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_IncomeStatementAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementAbstract" xlink:to="lab_us-gaap_IncomeStatementAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_39d2aaec-0ef7-4539-8cff-e877d172586f_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Hines Global Income Trust, Accumulated Other Comprehensive Income (Loss)</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">AOCI Attributable to Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_CostOfPropertyManagementFee_b743df2f-f0d9-476a-aab3-ab44ae6c4f2b_terseLabel_en-US" xlink:label="lab_hgit_CostOfPropertyManagementFee" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Property management fees</link:label>
    <link:label id="lab_hgit_CostOfPropertyManagementFee_label_en-US" xlink:label="lab_hgit_CostOfPropertyManagementFee" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cost Of Property Management Fee</link:label>
    <link:label id="lab_hgit_CostOfPropertyManagementFee_documentation_en-US" xlink:label="lab_hgit_CostOfPropertyManagementFee" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cost Of Property Management Fee</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_CostOfPropertyManagementFee" xlink:href="hgit-20200930.xsd#hgit_CostOfPropertyManagementFee"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_CostOfPropertyManagementFee" xlink:to="lab_hgit_CostOfPropertyManagementFee" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_350af6f6-7f99-458d-be64-89c69c5a0699_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">2024</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_LongTermDebtMaturityAfterYearFour_84331245-1b2f-44ca-9a1c-02ab4f2e5632_terseLabel_en-US" xlink:label="lab_hgit_LongTermDebtMaturityAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_hgit_LongTermDebtMaturityAfterYearFour_label_en-US" xlink:label="lab_hgit_LongTermDebtMaturityAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Long-Term Debt, Maturity, After Year Four</link:label>
    <link:label id="lab_hgit_LongTermDebtMaturityAfterYearFour_documentation_en-US" xlink:label="lab_hgit_LongTermDebtMaturityAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Long-Term Debt, Maturity, After Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_LongTermDebtMaturityAfterYearFour" xlink:href="hgit-20200930.xsd#hgit_LongTermDebtMaturityAfterYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_LongTermDebtMaturityAfterYearFour" xlink:to="lab_hgit_LongTermDebtMaturityAfterYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_c6c183eb-1277-416e-ad7d-f06dcf849067_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Segment Reporting Information, by Segment [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Segment Reporting Information, by Segment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:to="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfAboveAndBelowMarketLeases_38e77a15-30d0-49b2-9d1b-959fe2aa7df0_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfAboveAndBelowMarketLeases" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Amortization of above and below market leases</link:label>
    <link:label id="lab_us-gaap_AmortizationOfAboveAndBelowMarketLeases_label_en-US" xlink:label="lab_us-gaap_AmortizationOfAboveAndBelowMarketLeases" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Amortization of above and below Market Leases</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfAboveAndBelowMarketLeases" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_AmortizationOfAboveAndBelowMarketLeases"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfAboveAndBelowMarketLeases" xlink:to="lab_us-gaap_AmortizationOfAboveAndBelowMarketLeases" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable_9477e162-dd69-4c69-9b55-686e16bd8632_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Disposal Groups, Including Discontinued Operations [Table]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable_label_en-US" xlink:label="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Disposal Groups, Including Discontinued Operations [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xlink:to="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentIncomeInterest_d4b286fd-966e-4f6d-a54a-cb701dc3e3eb_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Interest and other income</link:label>
    <link:label id="lab_us-gaap_InvestmentIncomeInterest_b1c18105-57f2-4c1c-9247-ac94f964f8ea_negatedLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInterest" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Interest and other income</link:label>
    <link:label id="lab_us-gaap_InvestmentIncomeInterest_label_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Investment Income, Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeInterest" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_InvestmentIncomeInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentIncomeInterest" xlink:to="lab_us-gaap_InvestmentIncomeInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_SellingCommissionsDealerManagerFeesandDistributionandStockholderServicingFees_db4087d1-324a-44dc-8136-49fe6df253b3_negatedTerseLabel_en-US" xlink:label="lab_hgit_SellingCommissionsDealerManagerFeesandDistributionandStockholderServicingFees" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Selling commissions, dealer manager fees and distribution and stockholder servicing fees</link:label>
    <link:label id="lab_hgit_SellingCommissionsDealerManagerFeesandDistributionandStockholderServicingFees_label_en-US" xlink:label="lab_hgit_SellingCommissionsDealerManagerFeesandDistributionandStockholderServicingFees" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Selling Commissions, Dealer Manager Fees, and Distribution and Stockholder Servicing Fees</link:label>
    <link:label id="lab_hgit_SellingCommissionsDealerManagerFeesandDistributionandStockholderServicingFees_documentation_en-US" xlink:label="lab_hgit_SellingCommissionsDealerManagerFeesandDistributionandStockholderServicingFees" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Selling commissions, dealer manager fees, and distribution and stockholder servicing fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_SellingCommissionsDealerManagerFeesandDistributionandStockholderServicingFees" xlink:href="hgit-20200930.xsd#hgit_SellingCommissionsDealerManagerFeesandDistributionandStockholderServicingFees"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_SellingCommissionsDealerManagerFeesandDistributionandStockholderServicingFees" xlink:to="lab_hgit_SellingCommissionsDealerManagerFeesandDistributionandStockholderServicingFees" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Dividends_bcec3914-fcd2-4d66-b8e5-7aec605d2ef3_totalLabel_en-US" xlink:label="lab_us-gaap_Dividends" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total Declared</link:label>
    <link:label id="lab_us-gaap_Dividends_label_en-US" xlink:label="lab_us-gaap_Dividends" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Dividends</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Dividends" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_Dividends"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Dividends" xlink:to="lab_us-gaap_Dividends" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_RentReliefProvidedToTenantsByDeferral_a1104b41-7e6f-4775-9ba5-86d860edb720_terseLabel_en-US" xlink:label="lab_hgit_RentReliefProvidedToTenantsByDeferral" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Rent relief provided to tenants, by deferral</link:label>
    <link:label id="lab_hgit_RentReliefProvidedToTenantsByDeferral_label_en-US" xlink:label="lab_hgit_RentReliefProvidedToTenantsByDeferral" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Rent relief provided to tenants, by deferral</link:label>
    <link:label id="lab_hgit_RentReliefProvidedToTenantsByDeferral_documentation_en-US" xlink:label="lab_hgit_RentReliefProvidedToTenantsByDeferral" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Tenant rent that has been deferred until future periods.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_RentReliefProvidedToTenantsByDeferral" xlink:href="hgit-20200930.xsd#hgit_RentReliefProvidedToTenantsByDeferral"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_RentReliefProvidedToTenantsByDeferral" xlink:to="lab_hgit_RentReliefProvidedToTenantsByDeferral" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_ad13e6a1-5ac1-4b36-9dc3-dd02ff096dc6_totalLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Comprehensive income (loss) attributable to common stockholders</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ComprehensiveIncomeNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:to="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_3f5f74f1-9c2b-4e48-a4b6-76b77fdbd9d5_verboseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred stock, par value (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_PreferredStockParOrStatedValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:to="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_5f836325-4a6c-4a31-a2c9-fb2faaf57ca2_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">2021</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Long-Term Debt, Maturity, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestRateCapMember_81293545-eb81-46b3-b30a-fd96fe3206c0_terseLabel_en-US" xlink:label="lab_us-gaap_InterestRateCapMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Interest Rate Cap</link:label>
    <link:label id="lab_us-gaap_InterestRateCapMember_label_en-US" xlink:label="lab_us-gaap_InterestRateCapMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Interest Rate Cap [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestRateCapMember" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_InterestRateCapMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestRateCapMember" xlink:to="lab_us-gaap_InterestRateCapMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LegalEntityAxis_cc3a5052-5882-46f5-92fe-14d9bcd2fdc3_terseLabel_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:label id="lab_dei_LegalEntityAxis_label_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LegalEntityAxis" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_LegalEntityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LegalEntityAxis" xlink:to="lab_dei_LegalEntityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CityAreaCode_4f1bd452-6a5e-46ce-a719-802d1c8698c9_terseLabel_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">City Area Code</link:label>
    <link:label id="lab_dei_CityAreaCode_label_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">City Area Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_CityAreaCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CityAreaCode" xlink:to="lab_dei_CityAreaCode" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidationItemsDomain_be741de3-dd9b-41b9-8a24-943fc1164c2a_terseLabel_en-US" xlink:label="lab_srt_ConsolidationItemsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Consolidation Items [Domain]</link:label>
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    <link:label id="lab_hgit_SellingCommissionsMember_8e5d116f-9e8e-45fb-94c2-ea841d4912f6_terseLabel_en-US" xlink:label="lab_hgit_SellingCommissionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Selling Commissions</link:label>
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    <link:label id="lab_hgit_SellingCommissionsMember_documentation_en-US" xlink:label="lab_hgit_SellingCommissionsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Selling Commissions [Member]</link:label>
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    <link:label id="lab_country_NL_2a5abf29-10a5-41d5-af0f-0a461bb572a9_terseLabel_en-US" xlink:label="lab_country_NL" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">The Netherlands</link:label>
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    <link:label id="lab_dei_DocumentPeriodEndDate_339d3e0e-502f-4249-9556-3bed062f4b51_terseLabel_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Document Period End Date</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfDividendsPayableTextBlock_917f4f41-7a46-4bf0-a5b1-d55d629e1fd4_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDividendsPayableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Distributions</link:label>
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    <link:label id="lab_hgit_RookwoodPavilionMember_0fd6baf2-48c6-435e-9888-23dcffc2ca67_terseLabel_en-US" xlink:label="lab_hgit_RookwoodPavilionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Rookwood Pavilion</link:label>
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    <link:label id="lab_hgit_DealerManagerMember_4f4e1569-e317-49e7-8690-1434ec9a9168_terseLabel_en-US" xlink:label="lab_hgit_DealerManagerMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Dealer Manager</link:label>
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    <link:label id="lab_hgit_DealerManagerMember_documentation_en-US" xlink:label="lab_hgit_DealerManagerMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">The Dealer Manager, Hines Securities, Inc.</link:label>
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    <link:label id="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax_11ac1699-f722-4ab4-b268-3092eabb92b4_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Gain (loss) on derivative instruments</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfitLoss" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ProfitLoss"/>
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    <link:label id="lab_hgit_NonCashSellingCommissionDealerManagerFeesandDistributionandShareholderFeesPayable_5a82f8c1-5646-4e39-b2ee-5e1980fec9af_terseLabel_en-US" xlink:label="lab_hgit_NonCashSellingCommissionDealerManagerFeesandDistributionandShareholderFeesPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Distribution and stockholder servicing fees payable to the Dealer Manager</link:label>
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    <link:label id="lab_hgit_AssetDispositionAxisDomain_07fbff98-0343-46cb-ab68-172942d7ef5f_terseLabel_en-US" xlink:label="lab_hgit_AssetDispositionAxisDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset Disposition [Axis] [Domain]</link:label>
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    <link:label id="lab_us-gaap_RealEstateTaxExpense_8cee7758-87bd-4064-bfd9-c5607c502095_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateTaxExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Real property taxes</link:label>
    <link:label id="lab_us-gaap_RealEstateTaxExpense_label_en-US" xlink:label="lab_us-gaap_RealEstateTaxExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Real Estate Tax Expense</link:label>
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    <link:label id="lab_hgit_DSGBristolMember_f729daa1-9840-4610-9977-f2b1b54e1567_terseLabel_en-US" xlink:label="lab_hgit_DSGBristolMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">DSG Bristol</link:label>
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    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_5d07e238-4140-45ca-94f8-e9e3e0d774ef_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Long-term Debt, Type [Domain]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeDomain" xlink:to="lab_us-gaap_LongtermDebtTypeDomain" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Long-Term Debt, Maturity, Remainder of Fiscal Year</link:label>
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    <link:label id="lab_dei_EntityDomain_16bf8f9e-2e44-4835-ab45-af4d20ad3c1a_terseLabel_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity [Domain]</link:label>
    <link:label id="lab_dei_EntityDomain_label_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityDomain" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_EntityDomain"/>
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    <link:label id="lab_hgit_ContractDomain_fdd1e0ff-248e-46fe-a466-d66bef3ff0be_terseLabel_en-US" xlink:label="lab_hgit_ContractDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract [Domain]</link:label>
    <link:label id="lab_hgit_ContractDomain_label_en-US" xlink:label="lab_hgit_ContractDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract [Domain]</link:label>
    <link:label id="lab_hgit_ContractDomain_documentation_en-US" xlink:label="lab_hgit_ContractDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">[Domain] for Contract [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_ContractDomain" xlink:href="hgit-20200930.xsd#hgit_ContractDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_ContractDomain" xlink:to="lab_hgit_ContractDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CoverAbstract_bd6f7f6e-60c4-4b92-8ca9-38afb2c4a3fb_terseLabel_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cover [Abstract]</link:label>
    <link:label id="lab_dei_CoverAbstract_label_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cover [Abstract]</link:label>
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    <link:label id="lab_hgit_ConstructionManagementFeesMember_4bd713e7-a025-4162-9b71-21fb2571fbbe_terseLabel_en-US" xlink:label="lab_hgit_ConstructionManagementFeesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Development and Construction Management Fees</link:label>
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    <link:label id="lab_hgit_ConstructionManagementFeesMember_documentation_en-US" xlink:label="lab_hgit_ConstructionManagementFeesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Construction Management Fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_ConstructionManagementFeesMember" xlink:href="hgit-20200930.xsd#hgit_ConstructionManagementFeesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_ConstructionManagementFeesMember" xlink:to="lab_hgit_ConstructionManagementFeesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TradingSecuritiesDebt_5a44ac6c-c803-4253-a672-e3c26f2138ed_terseLabel_en-US" xlink:label="lab_us-gaap_TradingSecuritiesDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Investments in real estate-related securities</link:label>
    <link:label id="lab_us-gaap_TradingSecuritiesDebt_label_en-US" xlink:label="lab_us-gaap_TradingSecuritiesDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Securities, Trading</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TradingSecuritiesDebt" xlink:to="lab_us-gaap_TradingSecuritiesDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_CommonClassTXMember_fce5631b-b50c-4c30-8202-97138d17f28e_terseLabel_en-US" xlink:label="lab_hgit_CommonClassTXMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Class TX</link:label>
    <link:label id="lab_hgit_CommonClassTXMember_label_en-US" xlink:label="lab_hgit_CommonClassTXMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Class TX [Member]</link:label>
    <link:label id="lab_hgit_CommonClassTXMember_documentation_en-US" xlink:label="lab_hgit_CommonClassTXMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Class TX [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_CommonClassTXMember" xlink:to="lab_hgit_CommonClassTXMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract_9a23d3e9-bc63-4b7b-9be4-4f2a397fb142_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Financial Liabilities Fair Value Disclosure</link:label>
    <link:label id="lab_us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Financial Liabilities Fair Value Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract" xlink:to="lab_us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_DebtInstrumentMandatoryDrawFromFaceAmount_89b8079f-d80c-4f34-85b2-d7478bbfd2b0_terseLabel_en-US" xlink:label="lab_hgit_DebtInstrumentMandatoryDrawFromFaceAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Mandatory draw amount from face</link:label>
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    <link:label id="lab_hgit_DebtInstrumentMandatoryDrawFromFaceAmount_documentation_en-US" xlink:label="lab_hgit_DebtInstrumentMandatoryDrawFromFaceAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Portion of Debt Instrument Face Amount required by debt agreement to be drawn by agreed-upon date.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_DebtInstrumentMandatoryDrawFromFaceAmount" xlink:href="hgit-20200930.xsd#hgit_DebtInstrumentMandatoryDrawFromFaceAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_DebtInstrumentMandatoryDrawFromFaceAmount" xlink:to="lab_hgit_DebtInstrumentMandatoryDrawFromFaceAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_272ce8c0-abc0-4ea1-b9f5-d031fe9bb59c_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresAbstract" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_FairValueDisclosuresAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresAbstract" xlink:to="lab_us-gaap_FairValueDisclosuresAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeasesAcquiredInPlaceMember_1f37b477-7311-41fa-8595-3b1b66297a3c_terseLabel_en-US" xlink:label="lab_us-gaap_LeasesAcquiredInPlaceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">In-Place Leases</link:label>
    <link:label id="lab_us-gaap_LeasesAcquiredInPlaceMember_label_en-US" xlink:label="lab_us-gaap_LeasesAcquiredInPlaceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Leases, Acquired-in-Place [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeasesAcquiredInPlaceMember" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_LeasesAcquiredInPlaceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeasesAcquiredInPlaceMember" xlink:to="lab_us-gaap_LeasesAcquiredInPlaceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalents_89c33b38-e786-4f6c-8200-22eb24aa0420_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Restricted cash</link:label>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalents_label_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Restricted Cash and Cash Equivalents</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCashAndCashEquivalents" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_RestrictedCashAndCashEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedCashAndCashEquivalents" xlink:to="lab_us-gaap_RestrictedCashAndCashEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsLiabilitiesNet_e9b36cbf-abae-41b4-8311-0766fcab84bc_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Deferred tax assets</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsLiabilitiesNet_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Deferred Tax Assets, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsLiabilitiesNet" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DeferredTaxAssetsLiabilitiesNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsLiabilitiesNet" xlink:to="lab_us-gaap_DeferredTaxAssetsLiabilitiesNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskByBenchmarkAxis_df7c677a-c799-4568-8514-cb9c2354d95d_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Concentration Risk Benchmark [Axis]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ConcentrationRiskByBenchmarkAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:to="lab_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CostsAndExpenses_dd802507-3c31-49cd-9044-69905425979c_totalLabel_en-US" xlink:label="lab_us-gaap_CostsAndExpenses" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total expenses</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CostsAndExpenses" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_CostsAndExpenses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CostsAndExpenses" xlink:to="lab_us-gaap_CostsAndExpenses" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupHeldForSaleOrDisposedOfBySaleNotDiscontinuedOperationsMember_1106d72e-40c1-48c7-b979-a70dd8cce812_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupHeldForSaleOrDisposedOfBySaleNotDiscontinuedOperationsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Disposal Group, Held-for-sale or Disposed of by Sale, Not Discontinued Operations</link:label>
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    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_8302c906-805c-4723-8dcb-7f8533da20ee_terseLabel_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statement, Equity Components [Axis]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_StatementEquityComponentsAxis"/>
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    <link:label id="lab_hgit_IncomeTaxExpenseBenefitSaleOfRealEstate_905d8277-e9b8-4083-ac54-b3676196cbff_negatedTerseLabel_en-US" xlink:label="lab_hgit_IncomeTaxExpenseBenefitSaleOfRealEstate" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Provision for income taxes related to sale of real estate</link:label>
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    <link:label id="lab_us-gaap_AdditionalPaidInCapitalCommonStock_7f7fa79c-d206-4a0b-b2a3-53f4a146cc7c_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalCommonStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Additional paid-in capital</link:label>
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    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_67044e4f-0787-48e4-bb6d-07a69a64b161_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeTable" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DerivativeTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeTable" xlink:to="lab_us-gaap_DerivativeTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionLineItems_a9a79ead-2061-477f-9060-f21e6faf8d10_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Business Acquisition</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems" xlink:to="lab_us-gaap_BusinessAcquisitionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_7b8c7766-9f0c-4da5-8f50-022daa917847_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:to="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateInvestmentPropertyAtCost_49c78cab-4cdd-4b75-bbbd-24f45a48ff33_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentPropertyAtCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Investment property, gross</link:label>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities_b3c0e5d9-c123-4195-86fa-a742e4fc92a1_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Change in other liabilities</link:label>
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    <link:label id="lab_hgit_MaintalLogisticsMember_618810d2-b819-488b-b6a6-1b07cfb70cda_terseLabel_en-US" xlink:label="lab_hgit_MaintalLogisticsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Maintal Logistics</link:label>
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    <link:label id="lab_us-gaap_RecoveryOfDirectCosts_fbf49127-bf63-4138-893b-1b49b1c1148f_terseLabel_en-US" xlink:label="lab_us-gaap_RecoveryOfDirectCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Recovery revenue</link:label>
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    <link:label id="lab_hgit_DomainApartmentsMember_c5ed262a-9e7b-4002-bcd8-af12e1f9ddce_terseLabel_en-US" xlink:label="lab_hgit_DomainApartmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Domain Apartments</link:label>
    <link:label id="lab_hgit_DomainApartmentsMember_label_en-US" xlink:label="lab_hgit_DomainApartmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Domain Apartments [Member]</link:label>
    <link:label id="lab_hgit_DomainApartmentsMember_documentation_en-US" xlink:label="lab_hgit_DomainApartmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Domain Apartments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_DomainApartmentsMember" xlink:href="hgit-20200930.xsd#hgit_DomainApartmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_DomainApartmentsMember" xlink:to="lab_hgit_DomainApartmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_3b95215c-7eaf-4c03-b495-aba7e3373b11_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Number of reportable segments</link:label>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Number of Reportable Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfReportableSegments" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_NumberOfReportableSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfReportableSegments" xlink:to="lab_us-gaap_NumberOfReportableSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_NotesPayableIncludingRelatedPartyGross_9eff8eab-624f-4f42-b52d-13c8f549d74a_terseLabel_en-US" xlink:label="lab_hgit_NotesPayableIncludingRelatedPartyGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Notes payable including related party, gross</link:label>
    <link:label id="lab_hgit_NotesPayableIncludingRelatedPartyGross_1b171ff4-8f7e-4933-9492-72bbc77aa30e_totalLabel_en-US" xlink:label="lab_hgit_NotesPayableIncludingRelatedPartyGross" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Notes payable including related party, gross</link:label>
    <link:label id="lab_hgit_NotesPayableIncludingRelatedPartyGross_a52e38e8-ded9-48b8-beb2-5c2f4044ccb4_verboseLabel_en-US" xlink:label="lab_hgit_NotesPayableIncludingRelatedPartyGross" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Notes payable, book value</link:label>
    <link:label id="lab_hgit_NotesPayableIncludingRelatedPartyGross_label_en-US" xlink:label="lab_hgit_NotesPayableIncludingRelatedPartyGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Notes Payable Including Related Party, Gross</link:label>
    <link:label id="lab_hgit_NotesPayableIncludingRelatedPartyGross_documentation_en-US" xlink:label="lab_hgit_NotesPayableIncludingRelatedPartyGross" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Notes Payable Including Related Party, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_NotesPayableIncludingRelatedPartyGross" xlink:href="hgit-20200930.xsd#hgit_NotesPayableIncludingRelatedPartyGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_NotesPayableIncludingRelatedPartyGross" xlink:to="lab_hgit_NotesPayableIncludingRelatedPartyGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInSecurityDeposits_2ae00780-8977-46d8-b4ac-1c01e07542c1_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInSecurityDeposits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Change in security deposit liability</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInSecurityDeposits_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInSecurityDeposits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Increase (Decrease) in Security Deposits</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInSecurityDeposits" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_IncreaseDecreaseInSecurityDeposits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInSecurityDeposits" xlink:to="lab_us-gaap_IncreaseDecreaseInSecurityDeposits" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage_51752863-8d9b-494f-970d-d990ac3db592_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Interest rate</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Instrument, Interest Rate, Effective Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DebtInstrumentInterestRateEffectivePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:to="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidationItemsAxis_0b2e87d6-1889-482f-875c-4cc5a796ed3a_terseLabel_en-US" xlink:label="lab_srt_ConsolidationItemsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Consolidation Items [Axis]</link:label>
    <link:label id="lab_srt_ConsolidationItemsAxis_label_en-US" xlink:label="lab_srt_ConsolidationItemsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Consolidation Items [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsAxis" xlink:href="http://xbrl.fasb.org/srt/2020/elts/srt-2020-01-31.xsd#srt_ConsolidationItemsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidationItemsAxis" xlink:to="lab_srt_ConsolidationItemsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities_6ffcc5ad-933a-4030-ae6f-45bddee09cf2_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Conversion of common shares, value</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Stock Issued During Period, Value, Conversion of Convertible Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NondesignatedMember_49f35648-9e59-4146-8c4d-545865499057_terseLabel_en-US" xlink:label="lab_us-gaap_NondesignatedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Not Designated as Hedging Instrument</link:label>
    <link:label id="lab_us-gaap_NondesignatedMember_label_en-US" xlink:label="lab_us-gaap_NondesignatedMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Not Designated as Hedging Instrument [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NondesignatedMember" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_NondesignatedMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NondesignatedMember" xlink:to="lab_us-gaap_NondesignatedMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_45a78525-430e-49d7-9b5d-731654814764_terseLabel_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_label_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_EntityIncorporationStateCountryCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityIncorporationStateCountryCode" xlink:to="lab_dei_EntityIncorporationStateCountryCode" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredRentReceivablesNet_b5706f6d-0a2f-4c99-a43b-65d60e387a4f_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredRentReceivablesNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Straight-line rent receivable</link:label>
    <link:label id="lab_us-gaap_DeferredRentReceivablesNet_label_en-US" xlink:label="lab_us-gaap_DeferredRentReceivablesNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Deferred Rent Receivables, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredRentReceivablesNet" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DeferredRentReceivablesNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredRentReceivablesNet" xlink:to="lab_us-gaap_DeferredRentReceivablesNet" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain_ec2be4db-0487-4765-8391-101b3118ced0_terseLabel_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Real Estate [Domain]</link:label>
    <link:label id="lab_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain_label_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Real Estate [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain" xlink:href="http://xbrl.fasb.org/srt/2020/elts/srt-2020-01-31.xsd#srt_MortgageLoansOnRealEstateNamePropertyTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain" xlink:to="lab_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DepreciationAndAmortization_7630cdbe-f26d-44a9-b5d7-6508d7a007e6_verboseLabel_en-US" xlink:label="lab_us-gaap_DepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Depreciation and amortization</link:label>
    <link:label id="lab_us-gaap_DepreciationAndAmortization_1654c505-41da-4818-81e0-3bf03770ff05_terseLabel_en-US" xlink:label="lab_us-gaap_DepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Depreciation and amortization</link:label>
    <link:label id="lab_us-gaap_DepreciationAndAmortization_label_en-US" xlink:label="lab_us-gaap_DepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Depreciation, Depletion and Amortization, Nonproduction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DepreciationAndAmortization" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DepreciationAndAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DepreciationAndAmortization" xlink:to="lab_us-gaap_DepreciationAndAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_HinesMember_567db99d-5ee0-4bd8-8f2a-ebd3b867b20b_terseLabel_en-US" xlink:label="lab_hgit_HinesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Hines</link:label>
    <link:label id="lab_hgit_HinesMember_label_en-US" xlink:label="lab_hgit_HinesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Hines [Member]</link:label>
    <link:label id="lab_hgit_HinesMember_documentation_en-US" xlink:label="lab_hgit_HinesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Name of the related party</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_HinesMember" xlink:href="hgit-20200930.xsd#hgit_HinesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_HinesMember" xlink:to="lab_hgit_HinesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLeaseIncome_edfacc50-b962-434d-bfa1-632a7176eb28_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLeaseIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Rental revenue</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLeaseIncome_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLeaseIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Operating Lease, Lease Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLeaseIncome" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_OperatingLeaseLeaseIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLeaseIncome" xlink:to="lab_us-gaap_OperatingLeaseLeaseIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_RoyalMailMember_aa018931-15b4-4f68-a619-441d7f073f92_terseLabel_en-US" xlink:label="lab_hgit_RoyalMailMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Royal Mail</link:label>
    <link:label id="lab_hgit_RoyalMailMember_label_en-US" xlink:label="lab_hgit_RoyalMailMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Royal Mail [Member]</link:label>
    <link:label id="lab_hgit_RoyalMailMember_documentation_en-US" xlink:label="lab_hgit_RoyalMailMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Royal Mail</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_RoyalMailMember" xlink:href="hgit-20200930.xsd#hgit_RoyalMailMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_RoyalMailMember" xlink:to="lab_hgit_RoyalMailMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_39b24b2a-499c-4dc5-b7fb-82cf4442a649_terseLabel_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_label_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsidiarySaleOfStockAxis" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_SubsidiarySaleOfStockAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsidiarySaleOfStockAxis" xlink:to="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressPostalZipCode_21a158f3-0be8-4c37-bc29-a7ab352d3695_terseLabel_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:label id="lab_dei_EntityAddressPostalZipCode_label_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_EntityAddressPostalZipCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressPostalZipCode" xlink:to="lab_dei_EntityAddressPostalZipCode" xlink:type="arc" order="1"/>
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    <link:label id="lab_hgit_RookwoodCommonsMember_984c480c-83b5-4b93-854b-a32a4fb586fa_terseLabel_en-US" xlink:label="lab_hgit_RookwoodCommonsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Rookwood Commons</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_75e7c1f3-4187-4edb-8c3b-bd4682b48ef1_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Aggregate principal</link:label>
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    <link:label id="lab_hgit_LodzUrbanLogisticsMember_4d99a3bd-c763-4eb9-ac3f-47bbd4416113_terseLabel_en-US" xlink:label="lab_hgit_LodzUrbanLogisticsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">&#321;&#243;d&#378; Urban Logistics</link:label>
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    <link:label id="lab_us-gaap_BuildingAndBuildingImprovementsMember_ec0304e3-6051-4f2d-96cf-f148256cd9d9_terseLabel_en-US" xlink:label="lab_us-gaap_BuildingAndBuildingImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Buildings and Improvements</link:label>
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    <link:label id="lab_hgit_InternationalindustrialMember_59cfe8b7-4d27-4323-a9d6-982c254629c5_terseLabel_en-US" xlink:label="lab_hgit_InternationalindustrialMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">International industrial investments</link:label>
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    <link:label id="lab_us-gaap_RelatedPartyTransactionDueFromToRelatedPartyAbstract_832fc18d-9614-48d6-85e6-de8ee50158c6_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionDueFromToRelatedPartyAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Related Party Transactions</link:label>
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    <link:label id="lab_hgit_AssetsAndLiabilitiesHeldForSalePolicyTextBlock_f410146a-e1bf-46d5-a093-2e79b14cbced_terseLabel_en-US" xlink:label="lab_hgit_AssetsAndLiabilitiesHeldForSalePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Assets and Liabilities Held For Sale</link:label>
    <link:label id="lab_hgit_AssetsAndLiabilitiesHeldForSalePolicyTextBlock_label_en-US" xlink:label="lab_hgit_AssetsAndLiabilitiesHeldForSalePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Assets And Liabilities Held For Sale [Policy Text Block]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_hgit_AssetsAndLiabilitiesHeldForSalePolicyTextBlock" xlink:href="hgit-20200930.xsd#hgit_AssetsAndLiabilitiesHeldForSalePolicyTextBlock"/>
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    <link:label id="lab_us-gaap_EquityAbstract_3242de92-aa4c-45ab-9e09-40efd8840777_terseLabel_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Equity [Abstract]</link:label>
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    <link:label id="lab_us-gaap_DebtDisclosureAbstract_0a1817b4-499e-402b-806a-b6bb3fa242ae_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureAbstract" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DebtDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureAbstract" xlink:to="lab_us-gaap_DebtDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_AssetAcquisitionDomain_afd03a25-e210-40d1-9d08-3d9634cdcaf0_terseLabel_en-US" xlink:label="lab_hgit_AssetAcquisitionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset Acquisition [Domain]</link:label>
    <link:label id="lab_hgit_AssetAcquisitionDomain_label_en-US" xlink:label="lab_hgit_AssetAcquisitionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset Acquisition [Domain]</link:label>
    <link:label id="lab_hgit_AssetAcquisitionDomain_documentation_en-US" xlink:label="lab_hgit_AssetAcquisitionDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">[Domain] for Asset Acquisition [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_AssetAcquisitionDomain" xlink:href="hgit-20200930.xsd#hgit_AssetAcquisitionDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_AssetAcquisitionDomain" xlink:to="lab_hgit_AssetAcquisitionDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_AmendedCreditAgreementMaturingMay2021Member_3aa9a859-8257-49d2-9147-09cd88230640_terseLabel_en-US" xlink:label="lab_hgit_AmendedCreditAgreementMaturingMay2021Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Amended Credit Agreement, Maturing May 2021</link:label>
    <link:label id="lab_hgit_AmendedCreditAgreementMaturingMay2021Member_label_en-US" xlink:label="lab_hgit_AmendedCreditAgreementMaturingMay2021Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Amended Credit Agreement, Maturing May 2021 [Member]</link:label>
    <link:label id="lab_hgit_AmendedCreditAgreementMaturingMay2021Member_documentation_en-US" xlink:label="lab_hgit_AmendedCreditAgreementMaturingMay2021Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Amended Credit Agreement, Maturing May 2021</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_AmendedCreditAgreementMaturingMay2021Member" xlink:href="hgit-20200930.xsd#hgit_AmendedCreditAgreementMaturingMay2021Member"/>
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    <link:label id="lab_us-gaap_FinitelivedIntangibleAssetsAcquired1_cf59e5aa-900c-446b-b46e-c9245e37083b_terseLabel_en-US" xlink:label="lab_us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">In-place lease intangibles</link:label>
    <link:label id="lab_us-gaap_FinitelivedIntangibleAssetsAcquired1_label_en-US" xlink:label="lab_us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Finite-lived Intangible Assets Acquired</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_FinitelivedIntangibleAssetsAcquired1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:to="lab_us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_DeferredRentAllowanceForCreditLossDueToRentReliefProvidedToTenantByAbatement_165c8e82-1935-45d5-98a3-20a51e385e30_terseLabel_en-US" xlink:label="lab_hgit_DeferredRentAllowanceForCreditLossDueToRentReliefProvidedToTenantByAbatement" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Deferred rent, allowance for credit loss due to rent relief provided to tenant by abatement</link:label>
    <link:label id="lab_hgit_DeferredRentAllowanceForCreditLossDueToRentReliefProvidedToTenantByAbatement_label_en-US" xlink:label="lab_hgit_DeferredRentAllowanceForCreditLossDueToRentReliefProvidedToTenantByAbatement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Deferred rent, allowance for credit loss due to rent relief provided to tenant by abatement</link:label>
    <link:label id="lab_hgit_DeferredRentAllowanceForCreditLossDueToRentReliefProvidedToTenantByAbatement_documentation_en-US" xlink:label="lab_hgit_DeferredRentAllowanceForCreditLossDueToRentReliefProvidedToTenantByAbatement" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Deferred rent, allowance for credit loss due to rent relief provided to tenant by abatement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_DeferredRentAllowanceForCreditLossDueToRentReliefProvidedToTenantByAbatement" xlink:href="hgit-20200930.xsd#hgit_DeferredRentAllowanceForCreditLossDueToRentReliefProvidedToTenantByAbatement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_DeferredRentAllowanceForCreditLossDueToRentReliefProvidedToTenantByAbatement" xlink:to="lab_hgit_DeferredRentAllowanceForCreditLossDueToRentReliefProvidedToTenantByAbatement" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears_7a9c2594-b327-47e7-ae4b-5e161fab3932_terseLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">2024</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_d4322a09-7f9a-49c7-81be-fd64c52f7743_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net cash from (used in) financing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net Cash Provided by (Used in) Financing Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsCommonStock_6f0b779f-6ad1-415a-8cd1-d3be834ef023_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DividendsCommonStock" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Distributions declared</link:label>
    <link:label id="lab_us-gaap_DividendsCommonStock_label_en-US" xlink:label="lab_us-gaap_DividendsCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Dividends, Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsCommonStock" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DividendsCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsCommonStock" xlink:to="lab_us-gaap_DividendsCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_ContractAxis_23996b76-4702-4794-ae27-47f52e19717a_terseLabel_en-US" xlink:label="lab_hgit_ContractAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract [Axis]</link:label>
    <link:label id="lab_hgit_ContractAxis_label_en-US" xlink:label="lab_hgit_ContractAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract [Axis]</link:label>
    <link:label id="lab_hgit_ContractAxis_documentation_en-US" xlink:label="lab_hgit_ContractAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_ContractAxis" xlink:href="hgit-20200930.xsd#hgit_ContractAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_ContractAxis" xlink:to="lab_hgit_ContractAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems_960507f9-4e01-4aea-b35c-2253c16cdd6f_terseLabel_en-US" xlink:label="lab_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenues from External Customers and Long-Lived Assets [Line Items]</link:label>
    <link:label id="lab_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems_label_en-US" xlink:label="lab_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenues from External Customers and Long-Lived Assets [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems" xlink:to="lab_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_InternationalOfficeRealEstateInvestmentsMember_ae6fb765-7b45-468e-bfd2-338b3b98386a_terseLabel_en-US" xlink:label="lab_hgit_InternationalOfficeRealEstateInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">International office investments</link:label>
    <link:label id="lab_hgit_InternationalOfficeRealEstateInvestmentsMember_label_en-US" xlink:label="lab_hgit_InternationalOfficeRealEstateInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">International Office Real Estate Investments [Member]</link:label>
    <link:label id="lab_hgit_InternationalOfficeRealEstateInvestmentsMember_documentation_en-US" xlink:label="lab_hgit_InternationalOfficeRealEstateInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">International office real estate investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_InternationalOfficeRealEstateInvestmentsMember" xlink:href="hgit-20200930.xsd#hgit_InternationalOfficeRealEstateInvestmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_InternationalOfficeRealEstateInvestmentsMember" xlink:to="lab_hgit_InternationalOfficeRealEstateInvestmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockValue_21e97384-d33e-4b7e-a533-8e076cc58df0_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common shares, $0.001 par value per share (Note 6)</link:label>
    <link:label id="lab_us-gaap_CommonStockValue_label_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockValue" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_CommonStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockValue" xlink:to="lab_us-gaap_CommonStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems_7f83bb83-ca81-4dfd-8444-b88e0b6d0699_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Finite Lived Intangible Assets</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Finite-Lived Intangible Assets [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_FiniteLivedIntangibleAssetsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalYearFocus_f4b88d93-978d-44a4-9ebe-085f938f195e_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalYearFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalYearFocus" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_DocumentFiscalYearFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalYearFocus" xlink:to="lab_dei_DocumentFiscalYearFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesTradingRealizedGainLoss_4dfb1db6-0e01-409e-87b4-6940be16ba60_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesTradingRealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Realized gain (loss)</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesTradingRealizedGainLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesTradingRealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Securities, Trading, Realized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesTradingRealizedGainLoss" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DebtSecuritiesTradingRealizedGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesTradingRealizedGainLoss" xlink:to="lab_us-gaap_DebtSecuritiesTradingRealizedGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_55a5ef21-f6c3-4500-9363-042b05da30bd_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">2022</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:type="arc" order="1"/>
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    <link:label id="lab_hgit_OtherFeesMember_documentation_en-US" xlink:label="lab_hgit_OtherFeesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other Fees [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_OtherFeesMember" xlink:href="hgit-20200930.xsd#hgit_OtherFeesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_OtherFeesMember" xlink:to="lab_hgit_OtherFeesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable_6efe3be0-e940-461a-870f-21fd8bf7978d_terseLabel_en-US" xlink:label="lab_us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Subsidiary or Equity Method Investee, Sale of Stock by Subsidiary or Equity Investee [Table]</link:label>
    <link:label id="lab_us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable_label_en-US" xlink:label="lab_us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Subsidiary or Equity Method Investee, Sale of Stock by Subsidiary or Equity Investee [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" xlink:to="lab_us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingAbstract_8fbcd9df-2bc6-45bd-a60b-44a865c91c3e_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Segment Reporting [Abstract]</link:label>
    <link:label id="lab_us-gaap_SegmentReportingAbstract_label_en-US" xlink:label="lab_us-gaap_SegmentReportingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Segment Reporting [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingAbstract" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_SegmentReportingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingAbstract" xlink:to="lab_us-gaap_SegmentReportingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedAbstract_6ec39794-91c5-4539-a169-dc2b7ce563a7_terseLabel_en-US" xlink:label="lab_us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Reconciliation of Operating Profit (Loss) from Segments to Consolidated</link:label>
    <link:label id="lab_us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedAbstract_label_en-US" xlink:label="lab_us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Reconciliation of Operating Profit (Loss) from Segments to Consolidated [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedAbstract" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedAbstract" xlink:to="lab_us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseMember_92084307-0cb9-400f-97c0-dbd361ad27b8_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Interest Expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseMember_label_en-US" xlink:label="lab_us-gaap_InterestExpenseMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Interest Expense [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseMember" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_InterestExpenseMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseMember" xlink:to="lab_us-gaap_InterestExpenseMember" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_IncreaseDecreaseInTenantAndOtherReceivables_2426adda-f896-4549-a4d4-0d16fac3cd03_negatedTerseLabel_en-US" xlink:label="lab_hgit_IncreaseDecreaseInTenantAndOtherReceivables" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Change in tenant and other receivables</link:label>
    <link:label id="lab_hgit_IncreaseDecreaseInTenantAndOtherReceivables_label_en-US" xlink:label="lab_hgit_IncreaseDecreaseInTenantAndOtherReceivables" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Increase Decrease In Tenant And Other Receivables</link:label>
    <link:label id="lab_hgit_IncreaseDecreaseInTenantAndOtherReceivables_documentation_en-US" xlink:label="lab_hgit_IncreaseDecreaseInTenantAndOtherReceivables" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">The increase (decrease) during the reporting period in tenant and other receivables.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_IncreaseDecreaseInTenantAndOtherReceivables" xlink:href="hgit-20200930.xsd#hgit_IncreaseDecreaseInTenantAndOtherReceivables"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_IncreaseDecreaseInTenantAndOtherReceivables" xlink:to="lab_hgit_IncreaseDecreaseInTenantAndOtherReceivables" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_WakefieldLogisticsMember_dccfab06-8002-433f-a298-3ad556ee3ac2_terseLabel_en-US" xlink:label="lab_hgit_WakefieldLogisticsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Wakefield Logistics</link:label>
    <link:label id="lab_hgit_WakefieldLogisticsMember_label_en-US" xlink:label="lab_hgit_WakefieldLogisticsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Wakefield Logistics [Member]</link:label>
    <link:label id="lab_hgit_WakefieldLogisticsMember_documentation_en-US" xlink:label="lab_hgit_WakefieldLogisticsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Wakefield Logistics</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_WakefieldLogisticsMember" xlink:href="hgit-20200930.xsd#hgit_WakefieldLogisticsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_WakefieldLogisticsMember" xlink:to="lab_hgit_WakefieldLogisticsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_71c6aede-fee5-4767-a91b-019684d5569d_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Instrument</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentLineItems" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DebtInstrumentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentLineItems" xlink:to="lab_us-gaap_DebtInstrumentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_RentReliefProvidedToTenants_ac5e02cf-f043-4539-ba71-57bea7997066_terseLabel_en-US" xlink:label="lab_hgit_RentReliefProvidedToTenants" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Rent relief provided to tenants</link:label>
    <link:label id="lab_hgit_RentReliefProvidedToTenants_label_en-US" xlink:label="lab_hgit_RentReliefProvidedToTenants" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Rent relief provided to tenants</link:label>
    <link:label id="lab_hgit_RentReliefProvidedToTenants_documentation_en-US" xlink:label="lab_hgit_RentReliefProvidedToTenants" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Rent relief provided to tenants, including the abatement of rental payments and/or the deferral of rental payments due to later periods, as a result of their lost revenues resulting from the Coronavirus pandemic.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_RentReliefProvidedToTenants" xlink:href="hgit-20200930.xsd#hgit_RentReliefProvidedToTenants"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_RentReliefProvidedToTenants" xlink:to="lab_hgit_RentReliefProvidedToTenants" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquity_94d85acc-1ccc-4efe-b573-47f43b652268_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total stockholders&#8217; equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_label_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Stockholders' Equity Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_StockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquity" xlink:to="lab_us-gaap_StockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_GlasgowWestEndMember_ea388d5c-b2d4-4031-b860-d5cf964bc583_terseLabel_en-US" xlink:label="lab_hgit_GlasgowWestEndMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Glasgow West End</link:label>
    <link:label id="lab_hgit_GlasgowWestEndMember_label_en-US" xlink:label="lab_hgit_GlasgowWestEndMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Glasgow West End [Member]</link:label>
    <link:label id="lab_hgit_GlasgowWestEndMember_documentation_en-US" xlink:label="lab_hgit_GlasgowWestEndMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Glasgow West End [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_GlasgowWestEndMember" xlink:href="hgit-20200930.xsd#hgit_GlasgowWestEndMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_GlasgowWestEndMember" xlink:to="lab_hgit_GlasgowWestEndMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfStockIssuanceCosts_533bbe03-67ca-4474-8120-8cdc002b10ef_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfStockIssuanceCosts" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payment of offering costs</link:label>
    <link:label id="lab_us-gaap_PaymentsOfStockIssuanceCosts_label_en-US" xlink:label="lab_us-gaap_PaymentsOfStockIssuanceCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments of Stock Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfStockIssuanceCosts" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_PaymentsOfStockIssuanceCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfStockIssuanceCosts" xlink:to="lab_us-gaap_PaymentsOfStockIssuanceCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_9db31624-a72f-4272-93a8-77edf344cc9f_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total liabilities and equity</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Liabilities and Equity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_LiabilitiesAndStockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_18390989-b68f-40fc-9350-a1a2d6a1fd84_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accumulated other comprehensive income (loss)</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss), Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressCityOrTown_5e8c68e0-620c-483c-a4aa-879e545eb9c4_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:label id="lab_dei_EntityAddressCityOrTown_label_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_EntityAddressCityOrTown"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressCityOrTown" xlink:to="lab_dei_EntityAddressCityOrTown" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NotesPayable_51af9c17-b8df-4cec-9f42-be76c2f7a78f_terseLabel_en-US" xlink:label="lab_us-gaap_NotesPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Notes payable, net</link:label>
    <link:label id="lab_us-gaap_NotesPayable_label_en-US" xlink:label="lab_us-gaap_NotesPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Notes Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NotesPayable" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_NotesPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NotesPayable" xlink:to="lab_us-gaap_NotesPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_QueensCourtMember_66da8dcb-60c1-43da-b462-ca86b0849908_terseLabel_en-US" xlink:label="lab_hgit_QueensCourtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Queen's Court Student Residences</link:label>
    <link:label id="lab_hgit_QueensCourtMember_label_en-US" xlink:label="lab_hgit_QueensCourtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Queens Court [Member]</link:label>
    <link:label id="lab_hgit_QueensCourtMember_documentation_en-US" xlink:label="lab_hgit_QueensCourtMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Queens Court</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_QueensCourtMember" xlink:href="hgit-20200930.xsd#hgit_QueensCourtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_QueensCourtMember" xlink:to="lab_hgit_QueensCourtMember" xlink:type="arc" order="1"/>
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    <link:label id="lab_hgit_AssetDispositionAxis_documentation_en-US" xlink:label="lab_hgit_AssetDispositionAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset Disposition</link:label>
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    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_82772e6e-d7d5-4894-8bb9-57b2b3ff4373_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Long-term Debt, Type [Axis]</link:label>
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    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_80dbbf43-8b28-443d-a356-63f066d18da4_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Comprehensive (income) loss attributable to noncontrolling interests</link:label>
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    <link:label id="lab_us-gaap_DividendsAxis_0e2e21b0-e654-4e0f-8f2f-d2b578416f50_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Dividends [Axis]</link:label>
    <link:label id="lab_us-gaap_DividendsAxis_label_en-US" xlink:label="lab_us-gaap_DividendsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Dividends [Axis]</link:label>
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    <link:label id="lab_hgit_SecondOfferingMember_05e9863a-b27c-40db-95fc-b16f68cbc279_terseLabel_en-US" xlink:label="lab_hgit_SecondOfferingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Second Offering</link:label>
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    <link:label id="lab_hgit_SecondOfferingMember_documentation_en-US" xlink:label="lab_hgit_SecondOfferingMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Second Offering [Member]</link:label>
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    <link:label id="lab_us-gaap_AboveMarketLeasesMember_0eaca023-d91b-4aba-8c40-27b5c764726b_verboseLabel_en-US" xlink:label="lab_us-gaap_AboveMarketLeasesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Out-of-Market Lease Assets</link:label>
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    <link:label id="lab_hgit_IssuerCostsMember_af43f6bb-412f-44e5-b5e6-414ebc2332a7_terseLabel_en-US" xlink:label="lab_hgit_IssuerCostsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Organization and Offering Costs</link:label>
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    <link:label id="lab_us-gaap_StockholdersEquityAbstract_297e511e-8a2c-4d56-afd4-eee0271908fd_verboseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Stockholders&#8217; equity:</link:label>
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    <link:label id="lab_hgit_GoodyearCrossingIIMember_81e18539-e6c1-4599-a24c-e99d0821b132_terseLabel_en-US" xlink:label="lab_hgit_GoodyearCrossingIIMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Goodyear Crossing II</link:label>
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    <link:label id="lab_hgit_GoodyearCrossingIIMember_documentation_en-US" xlink:label="lab_hgit_GoodyearCrossingIIMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Goodyear Crossing II</link:label>
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    <link:label id="lab_us-gaap_ProductAndServiceOtherMember_9b25a254-e616-4955-879a-1d0da81f6f2d_terseLabel_en-US" xlink:label="lab_us-gaap_ProductAndServiceOtherMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other revenue</link:label>
    <link:label id="lab_us-gaap_ProductAndServiceOtherMember_label_en-US" xlink:label="lab_us-gaap_ProductAndServiceOtherMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Product and Service, Other [Member]</link:label>
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    <link:label id="lab_us-gaap_RelatedPartyTransactionsAbstract_7f7c818a-c6e2-4e01-a180-fbdd1846bd60_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Related Party Transactions [Abstract]</link:label>
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    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_7dbd1e9d-ba07-4fa2-a3e8-0268b93da7cc_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net change in cash, restricted cash and cash equivalents</link:label>
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    <link:label id="lab_hgit_DeferredFinancingCostsNetRevolvingCreditFacilities_2fb7372c-458e-4e7c-9f15-3c2d78e6fb0d_terseLabel_en-US" xlink:label="lab_hgit_DeferredFinancingCostsNetRevolvingCreditFacilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Deferred financing costs, net</link:label>
    <link:label id="lab_hgit_DeferredFinancingCostsNetRevolvingCreditFacilities_label_en-US" xlink:label="lab_hgit_DeferredFinancingCostsNetRevolvingCreditFacilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Deferred Financing Costs, Net, Revolving Credit Facilities</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_hgit_DeferredFinancingCostsNetRevolvingCreditFacilities" xlink:href="hgit-20200930.xsd#hgit_DeferredFinancingCostsNetRevolvingCreditFacilities"/>
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    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_5a6afab4-d6b5-45e8-b499-08727bc0633c_terseLabel_en-US" xlink:label="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Basis of Presentation</link:label>
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    <link:label id="lab_hgit_DepreciationAndAmortization1_d63597d1-227c-42b6-a045-33648a49187d_terseLabel_en-US" xlink:label="lab_hgit_DepreciationAndAmortization1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Depreciation and amortization</link:label>
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    <link:label id="lab_hgit_DepreciationAndAmortization1_documentation_en-US" xlink:label="lab_hgit_DepreciationAndAmortization1" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">The current period expense charged against earnings on long-lived, physical assets not used in production, and which are not intended for resale, to allocate or recognize the cost of such assets over their useful lives; or to record the reduction in book value of an intangible asset over the benefit period of such asset; or to reflect consumption during the period of an asset that is not used in production. Differs from the amount on the income statement due to the amortization of deferred financing costs and out of market leases that are recorded elsewhere on the cash flow statement.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_DepreciationAndAmortization1" xlink:href="hgit-20200930.xsd#hgit_DepreciationAndAmortization1"/>
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    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_6052af10-f88d-46f6-9038-ccd0326da0d0_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Variable rate</link:label>
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    <link:label id="lab_srt_OwnershipAxis_ec7dcee7-17c2-4fb6-ae46-9d4d4bdc94d6_terseLabel_en-US" xlink:label="lab_srt_OwnershipAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Ownership [Axis]</link:label>
    <link:label id="lab_srt_OwnershipAxis_label_en-US" xlink:label="lab_srt_OwnershipAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Ownership [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_OwnershipAxis" xlink:href="http://xbrl.fasb.org/srt/2020/elts/srt-2020-01-31.xsd#srt_OwnershipAxis"/>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_f6bdc58e-c221-48cf-a35e-c628792ded31_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Foreign currency translation adjustment</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_daf79b09-a6dc-410b-b5c8-2d6b538a2693_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Foreign currency translation adjustment</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Adjustment, Net of Tax</link:label>
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    <link:label id="lab_us-gaap_SaleOfStockNameOfTransactionDomain_7d09a29a-e593-4691-9770-396cef6a583a_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Sale of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_SaleOfStockNameOfTransactionDomain_label_en-US" xlink:label="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Sale of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_SaleOfStockNameOfTransactionDomain"/>
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    <link:label id="lab_srt_OwnershipDomain_6ac2e408-d456-4906-853d-a313a3584dd5_terseLabel_en-US" xlink:label="lab_srt_OwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Ownership [Domain]</link:label>
    <link:label id="lab_srt_OwnershipDomain_label_en-US" xlink:label="lab_srt_OwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Ownership [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_OwnershipDomain" xlink:href="http://xbrl.fasb.org/srt/2020/elts/srt-2020-01-31.xsd#srt_OwnershipDomain"/>
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    <link:label id="lab_hgit_AdvisorMember_859ee9c5-99a0-4438-a164-a56bdd3e5947_terseLabel_en-US" xlink:label="lab_hgit_AdvisorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">The Advisor</link:label>
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    <link:label id="lab_us-gaap_InterestPaidNet_aa8f29cd-bdcb-4d04-943d-f3b74c2ef927_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash paid for interest</link:label>
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    <link:label id="lab_us-gaap_DividendsPayableCurrentAndNoncurrent_2932da9e-0496-4a7a-bc93-bd54f407617d_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Distributions payable</link:label>
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    <link:label id="lab_us-gaap_DividendsPayableCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Dividends Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DividendsPayableCurrentAndNoncurrent"/>
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    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_e9cb2122-060d-495e-9ee9-1996f382f5bf_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total equity</link:label>
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    <link:label id="lab_us-gaap_DebtSecuritiesTradingGainLoss_27a81133-5ba8-4da4-aced-332351802173_totalLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesTradingGainLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total gain (loss) on real estate-related securities</link:label>
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    <link:label id="lab_us-gaap_DebtSecuritiesTradingGainLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesTradingGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Securities, Trading, Gain (Loss)</link:label>
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    <link:label id="lab_hgit_RentPaymentsMember_8bb0d2df-7a32-4183-a420-ae76e4cb5ed8_terseLabel_en-US" xlink:label="lab_hgit_RentPaymentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Rent Payments</link:label>
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    <link:label id="lab_us-gaap_RelatedPartyTransactionDomain_196ae2c2-3f47-4971-b35d-87af84f812be_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Related Party Transaction [Domain]</link:label>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets_6750aafa-16fa-4bc4-8b05-016c46b9768e_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Change in other assets</link:label>
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    <link:label id="lab_dei_EntityEmergingGrowthCompany_1ae580af-3f2e-4a40-9bbb-4c36db00fca6_terseLabel_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Emerging Growth Company</link:label>
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    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_2862e1e1-9247-4ff8-b0aa-e794cdb3306f_verboseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Maximum facility agreement amount</link:label>
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