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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-11-01</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001793360</rptOwnerCik>
            <rptOwnerName>Olson Kenneth Fletcher</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>Vice President</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-11-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1863</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>88598</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-11-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1806</value>
                    <footnoteId id="F3"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>3.46</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>86792</value>
                    <footnoteId id="F4"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">On November 1, 2019, the Reporting Person was granted an award of 16,949 restricted stock units with performance based vesting conditions based on the achievement of a relative total shareholder return of the Issuer's common stock from November 1, 2019 to the earlier of (i) November 1, 2020 or (ii) upon a change of control (measured relative to the NASDAQ Biotechnology index). The target number of the restricted stock units that may be earned was reported on the date of grant; the maximum amount is 150% of the number then reported. As a result of the Issuer's performance based on such performance targets, the reporting person earned 89% of the target amount, subject to continuation of employment through the remaining vesting dates. Accordingly, the reported transaction reflects the reduction of 1,863 performance restricted stock units from the target grant amount.</footnote>
        <footnote id="F2">Includes (a) the award described in footnote (1) above, (b) 36,756 restricted stock units that will vest on December 31, 2020, 2021, 2022 and 2023; and (c) 36,756 restricted stock units with performance based vesting conditions tied to relative total shareholder return.</footnote>
        <footnote id="F3">The shares were disposed of to satisfy the Reporting Person's tax withholding obligation in connection with a performance restricted stock unit award previously granted to the Reporting Person that vested in part on November 1, 2020.</footnote>
        <footnote id="F4">Includes (a) the shares and awards described in footnote (2) above, less (b) the disposition of shares reported in footnote (3) above.</footnote>
    </footnotes>

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

    <ownerSignature>
        <signatureName>/s/ David Sirois, by power of attorney</signatureName>
        <signatureDate>2020-11-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
