<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2022-01-14</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001848948</issuerCik>
        <issuerName>10X Capital Venture Acquisition Corp. III</issuerName>
        <issuerTradingSymbol>VCXB</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001861425</rptOwnerCik>
            <rptOwnerName>10X Capital SPAC Sponsor III LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O 10X CAPITAL VENTURE ACQUISITION CORP</rptOwnerStreet1>
            <rptOwnerStreet2>III, 1 WORLD TRADE CENTER, 85TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10007</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001916263</rptOwnerCik>
            <rptOwnerName>10X Capital Advisors, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O 10X CAPITAL VENTURE ACQUISITION CORP</rptOwnerStreet1>
            <rptOwnerStreet2>II, 1 WORLD TRADE CENTER, 85TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10007</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001828707</rptOwnerCik>
            <rptOwnerName>Thomas Hans</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>10X CAPITAL VENTURE ACQUISITION CORP</rptOwnerStreet1>
            <rptOwnerStreet2>II, 1 WORLD TRADE CENTER, 85TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10007</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Executive Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001828663</rptOwnerCik>
            <rptOwnerName>Weisburd David</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O 10X CAPITAL VENTURE ACQUISITION CORP</rptOwnerStreet1>
            <rptOwnerStreet2>II, 1 WORLD TRADE CENTER, 85TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10007</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>COO &amp; Head of Origination</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Class B Ordinary Shares</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2022-01-14</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>5000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Ordinary Shares</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>5000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>10000000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F3"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">On March 11, 2022, 10X Capital SPAC Sponsor III LLC (the &quot;Sponsor&quot;) forfeited at no cost 5,000 Class B ordinary shares of the Issuer in connection with the election by the underwriters of the Issuer's initial public offering of units to exercise an option granted to them to cover over-allotments in part and not in full.</footnote>
        <footnote id="F2">The Class B ordinary shares are convertible for the Issuer's Class A ordinary shares as described under the heading &quot;Description of Securities&quot; in the Issuer's Registration Statement on Form S-1 (File No. 333-253868) (the &quot;Registration Statement&quot;) and have no expiration date.</footnote>
        <footnote id="F3">The Sponsor is the record holder of the securities reported herein. 10X Capital Advisors, LLC is the manager of the Sponsor (the &quot;Manager&quot;). Mr. Thomas and Mr. Weisburd are the managing members of the Manager and have voting and investment discretion with respect to the securities held of record by the Sponsor.</footnote>
    </footnotes>

    <remarks>See Exhibit 99.1 - Joint Filer Information, which is incorporated herein by reference and describes in further detail the relationships of the Reporting Persons to the Issuer.</remarks>

    <ownerSignature>
        <signatureName>/s/ Joanna Heinz, Attorney-in-Fact for 10X Capital SPAC Sponsor III LLC</signatureName>
        <signatureDate>2022-03-11</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Joanna Heinz, Attorney-in-Fact for Hans Thomas</signatureName>
        <signatureDate>2022-03-11</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Hans Thomas, managing member for 10X Capital Advisors, LLC</signatureName>
        <signatureDate>2022-03-11</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Joanna Heinz, Attorney-in-Fact for David Weisburd</signatureName>
        <signatureDate>2022-03-11</signatureDate>
    </ownerSignature>
</ownershipDocument>
