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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-12-14</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001138315</rptOwnerCik>
            <rptOwnerName>KENNEDY JOHN F</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>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-12-14</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>5</transactionFormType>
                <transactionCode>G</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value>E</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>47687</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>262793</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">This transaction involved gifts of securities by the reporting person. Purchase price is not applicable as these transactions were bona fide gifts.</footnote>
        <footnote id="F2">Includes (a) a deferred stock award of 800 restricted stock units which vest on December 31, 2018; (b) a deferred stock award of 18,100 restricted stock units which fully vest on the earlier of (i) the date of the Issuer's next Annual Meeting of Stockholders after May 17, 2018, immediately prior to the commencement of such meeting, and (ii) May 17, 2019; (c) a deferred stock award of 3,475 restricted stock units which vest on December 31, 2018; and (d) 240,418 shares of common stock held by the Reporting Person.</footnote>
    </footnotes>

    <remarks>This form has been signed under power of attorney.</remarks>

    <ownerSignature>
        <signatureName>/s/ Chad Porter, by power of attorney</signatureName>
        <signatureDate>2018-12-18</signatureDate>
    </ownerSignature>
</ownershipDocument>
