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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-01-01</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001123494</issuerCik>
        <issuerName>HARVARD BIOSCIENCE INC</issuerName>
        <issuerTradingSymbol>HBIO</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001592266</rptOwnerCik>
            <rptOwnerName>Sun Yong</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O HARVARD BIOSCIENCE, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>84 OCTOBER HILL ROAD</rptOwnerStreet2>
            <rptOwnerCity>HOLLISTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>01746</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>VP - Strategic Marketing, R&amp;D</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-01-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1609</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>3.47</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>29674</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The shares were disposed to satisfy the Reporting Person's tax withholding obligation in connection with deferred stock awards previously granted to the Reporting Person which vested in part on January 1, 2016.</footnote>
        <footnote id="F2">Includes (a) a deferred stock award of 12,919 restricted stock units which shall vest in three equal installments on January 1, 2017, 2018 and 2019; (b) a deferred stock award of 14,058 restricted stock units with performance based vesting conditions, which shall vest on August 3, 2018 contingent upon achievement of a performance condition tied to relative total shareholder return; and (c) 2,697 shares of common stock held by the Reporting Person.</footnote>
    </footnotes>

    <remarks>The form is signed under power of attorney.</remarks>

    <ownerSignature>
        <signatureName>/s/ Chad Porter, by power of attorney</signatureName>
        <signatureDate>2016-01-05</signatureDate>
    </ownerSignature>
</ownershipDocument>
