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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-05-22</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001181100</rptOwnerCik>
            <rptOwnerName>MADISON DEARBORN PARTNERS LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O MADISON DEARBORN PARTNERS, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>70 W. MADISON STREET, SUITE 4600</rptOwnerStreet2>
            <rptOwnerCity>CHICAGO</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60602</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001344692</rptOwnerCik>
            <rptOwnerName>Madison Dearborn Capital Partners V - A L P</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O MADISON DEARBORN PARTNERS, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>70 W. MADISON STREET, SUITE 4600</rptOwnerStreet2>
            <rptOwnerCity>CHICAGO</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60602</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001344693</rptOwnerCik>
            <rptOwnerName>Madison Dearborn Capital Partners V - C L P</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O MADISON DEARBORN PARTNERS, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>70 W. MADISON STREET, SUITE 4600</rptOwnerStreet2>
            <rptOwnerCity>CHICAGO</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60602</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001362213</rptOwnerCik>
            <rptOwnerName>MADISON DEARBORN CAPITAL PARTNERS V EXECUTIVE-A L P</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O MADISON DEARBORN PARTNERS, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>70 W. MADISON STREET, SUITE 4600</rptOwnerStreet2>
            <rptOwnerCity>CHICAGO</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60602</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001416217</rptOwnerCik>
            <rptOwnerName>MDCP Co-Investors (CDW) LP</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O MADISON DEARBORN PARTNERS, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>70 W. MADISON STREET, SUITE 4600</rptOwnerStreet2>
            <rptOwnerCity>CHICAGO</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60602</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001579972</rptOwnerCik>
            <rptOwnerName>MADISON DEARBORN PARTNERS V-A&amp;C, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O MADISON DEARBORN PARTNERS, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>70 W. MADISON STREET, SUITE 4600</rptOwnerStreet2>
            <rptOwnerCity>CHICAGO</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60602</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001219630</rptOwnerCik>
            <rptOwnerName>MENCOFF SAMUEL M</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O MADISON DEARBORN PARTNERS, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>70 W. MADISON STREET, SUITE 4600</rptOwnerStreet2>
            <rptOwnerCity>CHICAGO</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60602</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</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>2015-05-22</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1061486</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>36.60</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>25622779</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $0.01</value>
            </securityTitle>
            <transactionDate>
                <value>2015-05-22</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>5967310</value>
                    <footnoteId id="F5"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>36.80</value>
                    <footnoteId id="F6"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>19655469</value>
                    <footnoteId id="F7"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F7"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Consists of 692,904 shares sold by Madison Dearborn Capital Partners V-A, L.P. (&quot;MDP A&quot;), 183,815 shares sold by Madison Dearborn Capital Partners V-C, L.P. (&quot;MDP C&quot;), 6,962 shares sold by Madison Dearborn Capital Partners V Executive-A, L.P. (&quot;MDP Exec&quot;) and 177,805 shares sold by MDCP Co-Investor (CDW), L.P. (&quot;MDP Co-Investor&quot;) to the Issuer in a stock repurchase.</footnote>
        <footnote id="F2">Consists of 16,725,710 shares held directly by MDP A, 4,437,042 shares held directly by MDP C, 168,061 shares held directly by MDP Exec and 4,291,966 shares held directly by MDCP Co-Investor.  Madison Dearborn Partners V-A&amp;C, L.P. (''MDP V'') is the general partner of MDP A, MDP C, MDP Exec and MDP Co-Investor. Madison Dearborn Partners, LLC (''MDP'') is the general partner of MDP V. As the sole members of a limited partner committee of MDP V that has the power, acting by majority vote, to vote or dispose of the shares directly held by MDP A, MDP C, MDP Exec and MDP Co-Investor, Paul J. Finnegan and Samuel M. Mencoff may be deemed to have shared voting and investment power over such shares. Each of Messrs. Finnegan and Mencoff and MDP V hereby disclaims any beneficial ownership of any shares held by MDP A, MDP C, MDP Exec and MDP Co-Investor except to the extent of its or his pecuniary interest therein.</footnote>
        <footnote id="F3">Mr. Mencoff has an indirect pecuniary interest in the shares of CDW Corporation's common stock held of record by the various MDP funds described above through his investment in MDP V. Each of MDP A, MDP C, MDP Exec and MDP Co-Investor and Mr. Mencoff may be deemed to share beneficial ownership of the reported securities and expressly disclaims beneficial ownership of such shares except to the extent of its or his pecuniary interest therein.</footnote>
        <footnote id="F4">Mr. Finnegan has separately filed a Form 4.</footnote>
        <footnote id="F5">Consists of 3,895,264 shares sold by MDP A, 1,033,346 shares sold by MDP C, 39,140 shares sold by MDP Exec and 999,560 shares sold by MDP Co-Investor in an underwritten secondary offering.</footnote>
        <footnote id="F6">This sale price reflects the public offering price.  The price received by the reporting persons will be reduced by the underwriters' commission of $0.20 per share.</footnote>
        <footnote id="F7">Consists of 12,830,446 shares held directly by MDP A, 3,403,696 shares held directly by MDP C, 128,921 shares held directly by MDP Exec and 3,292,406 shares held directly by MDCP Co-Investor.  MDP V is the general partner of MDP A, MDP C, MDP Exec and MDP Co-Investor. MDP is the general partner of MDP V. As the sole members of a limited partner committee of MDP V that has the power, acting by majority vote, to vote or dispose of the shares directly held by MDP A, MDP C, MDP Exec and MDP Co-Investor, Paul J. Finnegan and Samuel M. Mencoff may be deemed to have shared voting and investment power over such shares. Each of Messrs. Finnegan and Mencoff and MDP V hereby disclaims any beneficial ownership of any shares held by MDP A, MDP C, MDP Exec and MDP Co-Investor except to the extent of its or his pecuniary interest therein.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Madison Dearborn Partners LLC by /s/ James S. Rowe,  under Power of Attorney</signatureName>
        <signatureDate>2015-05-27</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Madison Dearborn Capital Partners V-A, L.P. by /s/ James S. Rowe,  under Power of Attorney</signatureName>
        <signatureDate>2015-05-27</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Madison Dearborn Capital Partners V-C, L.P. by /s/ James S. Rowe,  under Power of Attorney</signatureName>
        <signatureDate>2015-05-27</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Madison Dearborn Capital Partners V Executive-A, L.P. by /s/ James S. Rowe,  under Power of Attorney</signatureName>
        <signatureDate>2015-05-27</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>MDCP Co-Investors (CDW), L.P. by /s/ James S. Rowe,  under Power of Attorney</signatureName>
        <signatureDate>2015-05-27</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Madison Dearborn Partners V - A&amp;C, L.P. by /s/ James S. Rowe,  under Power of Attorney</signatureName>
        <signatureDate>2015-05-27</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Samuel M. Mencoff by /s/ James S. Rowe,  under Power of Attorney</signatureName>
        <signatureDate>2015-05-27</signatureDate>
    </ownerSignature>
</ownershipDocument>
