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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-11-30</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001059262</issuerCik>
        <issuerName>SP Plus Corp</issuerName>
        <issuerTradingSymbol>SP</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001559986</rptOwnerCik>
            <rptOwnerName>VCM STAN-CPC Holdings, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O VERSA CAPITAL MANAGEMENT, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>2929 ARCH STREET, 27TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>PHILADELPHIA</rptOwnerCity>
            <rptOwnerState>PA</rptOwnerState>
            <rptOwnerZipCode>19104</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001559987</rptOwnerCik>
            <rptOwnerName>Versa Capital Fund I, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O VERSA CAPITAL MANAGEMENT, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>2929 ARCH STREET, 27TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>PHILADELPHIA</rptOwnerCity>
            <rptOwnerState>PA</rptOwnerState>
            <rptOwnerZipCode>19104</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, par value $0.001 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2015-11-30</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>5900</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>25.2639</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>910787</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes></footnotes>

    <remarks>Versa Capital Fund I, L.P. is the managing member of VCM STAN-CPC Holdings, LLC. VCM STAN-CPC Holdings, LLC has appointed Paul Halpern to the board of directors of SP Plus Corporation.</remarks>

    <ownerSignature>
        <signatureName>/s/ VCM STAN-CPC HOLDINGS, LLC, by Thomas A. Kennedy, Secretary</signatureName>
        <signatureDate>2015-12-02</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ VERSA CAPITAL FUND I, L.P., by Thomas A. Kennedy, Authorized Person</signatureName>
        <signatureDate>2015-12-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
