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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-12-13</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001543643</issuerCik>
        <issuerName>CU Bancorp</issuerName>
        <issuerTradingSymbol>CUNB</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001555186</rptOwnerCik>
            <rptOwnerName>Rainer David I</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CU BANCORP 15821, VENTURA BLVD.</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 100</rptOwnerStreet2>
            <rptOwnerCity>ENCINO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>91436</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chairman &amp; CEO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-12-16</value>
                <footnoteId id="F1"/>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F2"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>3438</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>32.80</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>29108</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>182666</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Trustee of the David and Anne Rainer Trust</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>31634</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>IRA</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Restricted Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F4"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F5"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F5"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>40000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>40000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Options to Purchase Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>16.00</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F6"/>
            </exerciseDate>
            <expirationDate>
                <value>2017-09-24</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>23333</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>23333</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Options to Purchase Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>17.50</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F6"/>
            </exerciseDate>
            <expirationDate>
                <value>2017-02-26</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>4000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The Reporting Person is reporting this transaction late due to administrative error.</footnote>
        <footnote id="F2">The Reporting Person is reporting the withholding by CU Bancorp of 3,438 shares of common stock to satisfy the Reporting Person's tax withholding obligations in connection with the vesting of 7,753 shares of restricted stock to the Reporting Person on December 13, 2016, in accordance with the vesting schedule set forth in the restricted stock grant.</footnote>
        <footnote id="F3">Includes shares of restricted stock subject to a vesting schedule set forth in the restricted stock grant and subject to forfeiture upon the occurrence of certain events specified in the restricted stock grant.</footnote>
        <footnote id="F4">Each restricted stock unit represents a contingent right to receive one share of CUNB stock.</footnote>
        <footnote id="F5">The restricted stock units will vest in three(3) installments to which 20,000 shares will vest on March 19, 2017 and 10,000 shares will vest on each March 19, 2018 and 2019.  Vested shares will be delivered to the Reporting Person on or before March 15 in the calendar year following the vesting except to the extent that CUNB reasonably anticipates that CUNB's corporate income tax deduction for the payment of shares will be limited or eliminated as a result of the application of Internal Revenue Code Section 162(m).  CUNB will defer the payment and delivery of such shares to the earliest date where CUNB reasonably anticipates that such deduction will not be limited or eliminated by application of Internal Revenue Code Section 162(m).</footnote>
        <footnote id="F6">As of filing date, the stock option grant is 100% vested and immediately exercisable.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>David I. Rainer, By: Anita Y. Wolman, Attorney-in-Fact.</signatureName>
        <signatureDate>2016-12-23</signatureDate>
    </ownerSignature>
</ownershipDocument>
