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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-02-11</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001295401</issuerCik>
        <issuerName>Bancorp, Inc.</issuerName>
        <issuerTradingSymbol>TBBK</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001197257</rptOwnerCik>
            <rptOwnerName>EGGEMEYER JOHN M III</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CASTLE CREEK ADVISORS IV LLC</rptOwnerStreet1>
            <rptOwnerStreet2>6051 EL TORDO, PO BOX 1329</rptOwnerStreet2>
            <rptOwnerCity>RANCHO SANTA FE</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>92067</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2019-02-11</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>7500</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>30000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Foonote</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">These restricted stock units, each of which represents the right to receive one share of common stock of The Bancorp, Inc. (&quot;Common Stock&quot;), were issued to Castle Creek Advisors IV LLC (&quot;Advisors IV&quot;), on behalf of John M. Eggemeyer in his capacity as a member of the Board of Directors of The Bancorp, Inc. on February 11, 2019 and will become fully vested on February 11, 2020.</footnote>
        <footnote id="F2">These securities, which include (i) 15,000 shares of Common Stock and (ii) an additional 7,500 restricted stock units (which represent the right to receive one share of Common Stock and are scheduled to become fully vested on May 16, 2019), in each case previously issued to Advisors IV on behalf of John M. Eggemeyer in his capacity as a member of the Board of Directors of The Bancorp, Inc., are held directly by Advisors IV. The reporting person disclaims beneficial ownership of all of the securities held by Advisors IV, except to the extent of his respective pecuniary interest therein, and this report shall not be deemed an admission that the reporting person is the beneficial owner of such securities for purposes of Section 16 of the Securities Exchange Act of 1934, as amended, or for any other purpose.</footnote>
    </footnotes>

    <remarks>The reporting person is a managing principal of Castle Creek Capital VI LLC, the sole general partner of Castle Creek Capital Partners VI, LP (&quot;Fund VI&quot;).  As of February 12, 2019, Fund VI owned 3,576,598 shares of the Issuer's common stock (the &quot;Fund VI Shares&quot;). The reporting person disclaims beneficial ownership of the Fund VI Shares, and this report shall not be deemed an admission that the reporting person is the beneficial owner of the Fund VI Shares for purposes of Section 16 of the Securities Exchange Act of 1934, as amended, or for any other purpose.</remarks>

    <ownerSignature>
        <signatureName>/s/ John M. Eggemeyer</signatureName>
        <signatureDate>2019-02-12</signatureDate>
    </ownerSignature>
</ownershipDocument>
