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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-08-13</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001468328</issuerCik>
        <issuerName>Addus HomeCare Corp</issuerName>
        <issuerTradingSymbol>ADUS</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001256578</rptOwnerCik>
            <rptOwnerName>FIRST MARK L</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>6303 COWBOYS WAY</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 600</rptOwnerStreet2>
            <rptOwnerCity>FRISCO</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75034</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-08-13</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>475000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>94.26</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>566638</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>20222</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The reported securities are held by ECP Helios Partners III, L.P. (&quot;Helios III&quot;), ECP General III, L.P. (&quot;General III&quot;) and Eos Partners SBIC III, L.P. (&quot;SBIC III&quot;). Mark L. First is a director of the Issuer and a managing director of Eos Management, L.P. and its affiliates (&quot;Eos&quot;), which includes Helios III, General III and SBIC III. As a result, Mr. First may be deemed to share beneficial ownership of the securities owned by Eos. Mr. First disclaims beneficial ownership of such securities, except to the extent of his pecuniary interest therein, and this report shall not be deemed an admission that Mr. First is the beneficial owner of such securities for purposes of Section 16 or for any other purpose.</footnote>
        <footnote id="F2">Following the reported transactions, 207,582 shares are held by Helios III, 184,876 shares are held by General III and 174,180 shares are held by SBIC III (each rounded to the nearest whole share).</footnote>
    </footnotes>

    <remarks>Exhibit Index:  Exhibit 24 - Power of Attorney for Mark L. First dated November 30, 2016</remarks>

    <ownerSignature>
        <signatureName>/s/ Mark L. First</signatureName>
        <signatureDate>2020-08-14</signatureDate>
    </ownerSignature>
</ownershipDocument>
