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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-04-22</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001723648</issuerCik>
        <issuerName>Crescent Acquisition Corp</issuerName>
        <issuerTradingSymbol>CRSA</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001727828</rptOwnerCik>
            <rptOwnerName>CFI Sponsor LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CRESCENT ACQUISITION CORP,</rptOwnerStreet1>
            <rptOwnerStreet2>11100 SANTA MONICA BOULEVARD, SUITE 2000</rptOwnerStreet2>
            <rptOwnerCity>LOS ANGELES</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>90025</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001543594</rptOwnerCik>
            <rptOwnerName>Attanasio Mark</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CRESCENT ACQUISITION CORP,</rptOwnerStreet1>
            <rptOwnerStreet2>11100 SANTA MONICA BOULEVARD, SUITE 2000</rptOwnerStreet2>
            <rptOwnerCity>LOS ANGELES</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>90025</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001188302</rptOwnerCik>
            <rptOwnerName>BEYER ROBERT D</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CRESCENT ACQUISITION CORP,</rptOwnerStreet1>
            <rptOwnerStreet2>11100 SANTA MONICA BOULEVARD, SUITE 2000</rptOwnerStreet2>
            <rptOwnerCity>LOS ANGELES</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>90025</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Executive Chairman</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001105576</rptOwnerCik>
            <rptOwnerName>CHAPUS JEAN-MARC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CRESCENT ACQUISITION CORP,</rptOwnerStreet1>
            <rptOwnerStreet2>11100 SANTA MONICA BOULEVARD, SUITE 2000</rptOwnerStreet2>
            <rptOwnerCity>LOS ANGELES</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>90025</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chairman of the Board</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001758263</rptOwnerCik>
            <rptOwnerName>Purdy Todd M.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CRESCENT ACQUISITION CORP,</rptOwnerStreet1>
            <rptOwnerStreet2>11100 SANTA MONICA BOULEVARD, SUITE 2000</rptOwnerStreet2>
            <rptOwnerCity>LOS ANGELES</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>90025</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Executive Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001513857</rptOwnerCik>
            <rptOwnerName>Crescent Capital Group LP</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CRESCENT ACQUISITION CORP,</rptOwnerStreet1>
            <rptOwnerStreet2>11100 SANTA MONICA BOULEVARD, SUITE 2000</rptOwnerStreet2>
            <rptOwnerCity>LOS ANGELES</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>90025</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001727826</rptOwnerCik>
            <rptOwnerName>Beyer Family Interests LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CHAPARAL INVESTMENTS LLC,</rptOwnerStreet1>
            <rptOwnerStreet2>11601 WILSHIRE BOULEVARD, SUITE 1825</rptOwnerStreet2>
            <rptOwnerCity>LOS ANGELES</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>90025</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001769607</rptOwnerCik>
            <rptOwnerName>TSJD Family LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CRESCENT ACQUISITION CORP,</rptOwnerStreet1>
            <rptOwnerStreet2>11100 SANTA MONICA BOULEVARD, SUITE 2000</rptOwnerStreet2>
            <rptOwnerCity>LOS ANGELES</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>90025</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Class F Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2019-04-22</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>937500</value>
                    <footnoteId id="F3"/>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>937500</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>6175000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">As described in the issuer's registration statement on Form S-1 (File No. 333-229718) under the heading &quot;Description of Securities-Founder Shares,&quot; the shares of Class F common stock, par value $0.0001 per share (the &quot;Class F Shares&quot;), of the  issuer will automatically convert into shares of Class A common stock at the time of the issuer's initial business combination, or earlier at the option of the holder, on a one-for-one basis, subject to certain adjustment.</footnote>
        <footnote id="F2">CFI Sponsor LLC directly owns these Class F Shares. Messrs. Attanasio and Chapus control Crescent Capital Group LP, and Crescent Capital Group LP, an entity controlled by Mr. Beyer and an entity controlled by Mr. Purdy are the managing members of CFI Sponsor LLC. Accordingly, Messrs. Attanasio, Beyer, Chapus and Purdy share voting and dispositive power over the Class F Shares held by CFI Sponsor LLC and may be deemed to beneficially own such Class F Shares.</footnote>
        <footnote id="F3">This Form 4 reflects the cancellation by the issuer of 937,500 Class F Shares, which were automatically surrendered to the issuer for no consideration by the reporting person pursuant to contractual arrangements with the issuer, triggered by the election by the underwriters of the issuer's initial public offering not to exercise their option to purchase additional units.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ George P. Hawley, Attorney-in-Fact</signatureName>
        <signatureDate>2019-04-23</signatureDate>
    </ownerSignature>
</ownershipDocument>
