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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-05-06</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001504983</rptOwnerCik>
            <rptOwnerName>Gagnon Robert E.</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>Chief Financial Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-05-06</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>88652</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>153897</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-05-06</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>88652</value>
                    <footnoteId id="F3"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>242549</value>
                    <footnoteId id="F4"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Represents a deferred stock award of 88,652 restricted stock units which shall vest in four equal installments on January 1, 2017, 2018, 2019 and 2020.</footnote>
        <footnote id="F2">Includes (a) a deferred stock award of 88,652 restricted stock units which shall vest in four equal installments on January 1, 2017, 2018, 2019 and 2020; (b) a deferred stock award of 19,875 restricted stock units which shall vest in three equal installments on January 1, 2017, 2018 and 2019; (c) a deferred stock award of 28,117 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 (d) 17,253 shares of common stock held by the Reporting Person.</footnote>
        <footnote id="F3">Represents a deferred stock award of 88,652 restricted stock units which shall vest in full on May 6, 2018.</footnote>
        <footnote id="F4">Includes (a) a deferred stock award of 88,652 restricted stock units which shall vest in full on May 6, 2018; (b) a deferred stock award of 88,652 restricted stock units which shall vest in four equal installments on January 1, 2017, 2018, 2019 and 2020; (c) a deferred stock award of 19,875 restricted stock units which shall vest in three equal installments on January 1, 2017, 2018 and 2019; (d) a deferred stock award of 28,117 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 (e) 17,253 shares of common stock held by the Reporting Person.</footnote>
    </footnotes>

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

    <ownerSignature>
        <signatureName>/s/ Chad Porter, by power of attorney</signatureName>
        <signatureDate>2016-05-10</signatureDate>
    </ownerSignature>
</ownershipDocument>
