<?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>0001228774</rptOwnerCik>
            <rptOwnerName>KOZLOV HERSH</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>WOLF BLOCK SCHORR &amp; SOLIS</rptOwnerStreet1>
            <rptOwnerStreet2>1940 RTE 70 E</rptOwnerStreet2>
            <rptOwnerCity>CHERRY HILL</rptOwnerCity>
            <rptOwnerState>NJ</rptOwnerState>
            <rptOwnerZipCode>08003</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>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>85000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The Reporting Person was granted restricted stock units, each of which represents the right to receive one share of common stock of The Bancorp, Inc. upon vesting. The restricted stock units shall vest in one installment on the first anniversary of the date of grant.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/Paul Frenkiel, attorney-in-fact</signatureName>
        <signatureDate>2019-02-11</signatureDate>
    </ownerSignature>
</ownershipDocument>
