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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-08-17</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001666749</rptOwnerCik>
            <rptOwnerName>Castle Creek Capital Partners VI, LP</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CASTLE CREEK CAPITAL 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>
            <otherText>See Remarks</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001671438</rptOwnerCik>
            <rptOwnerName>Castle Creek Capital VI LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CASTLE CREEK CAPITAL 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>
            <otherText>See Remarks</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001197257</rptOwnerCik>
            <rptOwnerName>EGGEMEYER JOHN M III</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CASTLE CREEK CAPITAL 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>
            <otherText>See Remarks</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001242722</rptOwnerCik>
            <rptOwnerName>THOMAS J MIKESELL</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CASTLE CREEK CAPITAL 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>
            <otherText>See Remarks</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001332829</rptOwnerCik>
            <rptOwnerName>MERLO MARK G</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CASTLE CREEK CAPITAL 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>
            <otherText>See Remarks</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001481798</rptOwnerCik>
            <rptOwnerName>Pietrzak John</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CASTLE CREEK CAPITAL 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>
            <otherText>See Remarks</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2017-08-17</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>93700</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>7.4989</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3026598</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>15000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The price reported in Column 4 is a weighted average price. These shares were acquired in multiple transactions at prices ranging from $7.4700 to $7.5000, inclusive. The reporting persons undertake to provide to The Bancorp, Inc., any security holder of The Bancorp, Inc., or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares acquired at each separate price within the range set forth in footnote (1) to this Form 4.</footnote>
        <footnote id="F2">These securities are directly held by Castle Creek Capital Partners VI, LP (&quot;Fund VI&quot;).  Mr. Eggemeyer, Mr. Thomas, Mr. Merlo, and Mr. Pietrzak are managing principals of Castle Creek Capital VI LLC, the sole general partner of Fund VI.  Castle Creek Capital VI LLC, Mr. Eggemeyer, Mr. Thomas, Mr. Merlo, and Mr. Pietrzak each disclaim beneficial ownership of these shares of Common Stock, except to the extent of their respective pecuniary interest therein, and this report shall not be deemed an admission that Castle Creek Capital Partners VI LLC, Mr. Eggemeyer, Mr. Thomas, Mr. Merlo, or Mr. Pietrzak is the beneficial owner of such shares of Common Stock for purposes of Section 16 of the Securities Exchange Act of 1934, as amended, or for any other purpose.</footnote>
        <footnote id="F3">These restricted stock units, each of which represents the right to receive one share of common stock of The Bancorp, Inc., were previously issued to Castle Creek Advisors IV LLC, on behalf of John M. Eggemeyer in his capacity as a member of the Board of Directors of The Bancorp, Inc., and vest in three equal annual installments beginning on February 3, 2018.</footnote>
    </footnotes>

    <remarks>John M. Eggemeyer, a managing pricipal of Castle Creek Capital VI, LLC, serves on the Issuer's board of directors (the &quot;Board&quot;) as a representative of Castle Creek Capital Partners VI, LP (&quot;Fund VI&quot;), pursuant to Fund VI's contractual right to nominate a representative to the Board.  By virtue of his representation on the Board, for purposes of Section 16 of the Securities Exchange Act of 1934, as amended, the Reporting Persons are deemed to be directors of the Issuer by deputization.</remarks>

    <ownerSignature>
        <signatureName>CASTLE CREEK CAPITAL PARTNERS VI, LP, By: /s/ John M. Eggemeyer, Name: John M. Eggemeyer, Title: President</signatureName>
        <signatureDate>2017-08-18</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>CASTLE CREEK CAPITAL VI LLC, By: /s/ John M. Eggemeyer, Name: John M. Eggemeyer, Title: President</signatureName>
        <signatureDate>2017-08-18</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>JOHN M. EGGEMEYER, By: /s/ John M. Eggemeyer, Name: John M. Eggemeyer</signatureName>
        <signatureDate>2017-08-18</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>J. MIKESELL THOMAS, By: /s/ J. Mikesell Thomas, Name: J. Mikesell Thomas</signatureName>
        <signatureDate>2017-08-18</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>MARK G. MERLO, By: /s/ Mark G. Merlo, Name: Mark G. Merlo</signatureName>
        <signatureDate>2017-08-18</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>JOHN T. PIETRZAK, By: /s/ John T. Pietrzak, Name: John T. Pietrzak</signatureName>
        <signatureDate>2017-08-18</signatureDate>
    </ownerSignature>
</ownershipDocument>
