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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2019-03-07</periodOfReport>

    <noSecuritiesOwned>1</noSecuritiesOwned>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001640350</rptOwnerCik>
            <rptOwnerName>Wilhelms Mike</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>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>See Remarks</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <footnotes></footnotes>

    <remarks>Chief Financial Officer and Treasurer

Exhibit 24.1 - Power of Attorney</remarks>

    <ownerSignature>
        <signatureName>/s/ George P. Hawley, Attorney-in-Fact</signatureName>
        <signatureDate>2019-03-07</signatureDate>
    </ownerSignature>
</ownershipDocument>
