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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-08-17</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001280600</issuerCik>
        <issuerName>ACCELERON PHARMA INC</issuerName>
        <issuerTradingSymbol>XLRN</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001117003</rptOwnerCik>
            <rptOwnerName>MCGUIRE TERRANCE</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O POLARIS VENTURE PARTNERS</rptOwnerStreet1>
            <rptOwnerStreet2>1000 WINTER STREET</rptOwnerStreet2>
            <rptOwnerCity>WALTHAM</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02451</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>2015-08-17</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>407259</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>30.25</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1303232</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Represents 400,000 shares sold by Polaris Venture Partners IV, L.P. (&quot;PVP IV&quot;) and 7,259 shares sold by Polaris Venture Partners Entrepreneurs' Fund IV, L.P. (&quot;PVPE IV&quot; and, together with PVP IV, the &quot;Funds&quot;).</footnote>
        <footnote id="F2">The Reporting Person is a director of the Issuer and managing member of Polaris Venture Management Co. IV, L.L.C. (&quot;PVM IV&quot;), the general partner of each of PVP IV and PVPE IV.  The amount of securities beneficially owned as reported in column 5 represents 1,273,175 shares, 22,983 shares, and 7,074 shares that are held directly by PVP IV, PVPE IV and PVM IV, respectively following the transactions reported in this Form 4.  PVM IV disclaims beneficial ownership of the Funds' securities and this report shall not be deemed an admission that PVM IV is the beneficial owner of such securities for purposes of Section 16 or for any other purpose, except to the extent of its pecuniary interest, if any, therein. (Continued in Footnote 4)</footnote>
        <footnote id="F3">Each of Jonathan A. Flint and the Reporting Person are the managing members of PVM IV and each of them disclaims beneficial ownership of the Funds' and PVM IV's securities and this report shall not be deemed an admission that any of them is the beneficial owner of such securities for purposes of Section 16 or for any other purpose, except to the extent of their pecuniary interest, if any, therein.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Terrance McGuire</signatureName>
        <signatureDate>2015-08-19</signatureDate>
    </ownerSignature>
</ownershipDocument>
