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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2014-05-28</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001402057</issuerCik>
        <issuerName>CDW Corp</issuerName>
        <issuerTradingSymbol>CDW</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001084355</rptOwnerCik>
            <rptOwnerName>CREAMER GLENN M</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O PROVIDENCE EQUITY PARTNERS L.L.C.</rptOwnerStreet1>
            <rptOwnerStreet2>50 KENNEDY PLAZA, 18TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>PROVIDENCE</rptOwnerCity>
            <rptOwnerState>RI</rptOwnerState>
            <rptOwnerZipCode>02903</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $0.01</value>
            </securityTitle>
            <transactionDate>
                <value>2014-05-28</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>6835274</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>28.35</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>39431897</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Consists of 4,330,785 shares sold by Providence Equity Partners VI L.P. (&quot;PEP VI&quot;), 1,489,842 shares sold by Providence Equity Partners VI-A L.P. (&quot;PEP VI-A&quot;) and 1,014,647 shares sold by PEP Co-Investors (CDW) L.P. (&quot;PEP Co-Investor&quot;).</footnote>
        <footnote id="F2">This sale price reflects the public offering price. The price received by the reporting person will be reduced by the underwriter's commission of $0.15 per share.</footnote>
        <footnote id="F3">Consists of 24,983,785 shares held directly by PEP VI, 8,594,722 shares held directly by PEP VI-A and 5,853,390 shares held directly by PEP Co-Investor. The shares held by PEP VI, PEP VI-A and PEP Co-Investor may be deemed to be beneficially owned by Providence Equity GP VI L.P. (&quot;PEP GP&quot;), the general partner of PEP VI, PEP VI-A and PEP Co-Investor and Providence Equity Partners VI L.L.C. (&quot;PEP LLC&quot;), the general partner of PEP GP. Messrs. Jonathan Nelson, Glenn Creamer and Paul Salem are members of PEP LLC and may be deemed to have shared voting and investment power over such shares. Each of PEP LLC, PEP GP, and Messrs. Nelson, Creamer and Salem hereby disclaims any beneficial ownership of any shares held by PEP VI, PEP VI-A and PEP Co-Investor except to the extent of any pecuniary interest therein.</footnote>
        <footnote id="F4">The record and other beneficial owners have separately filed a Form 4.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ James S. Rowe,  under Power of Attorney</signatureName>
        <signatureDate>2014-05-30</signatureDate>
    </ownerSignature>
</ownershipDocument>
