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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-11-17</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>ONE MARINA PARK DRIVE, SUITE 1100</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>BOSTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02210</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>2016-11-17</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>693020</value>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>605133</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-11-18</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F5"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>6980</value>
                    <footnoteId id="F5"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>598153</value>
                    <footnoteId id="F6"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-11-18</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F5"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1624</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1624</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Represents a pro rata distribution, and not a purchase or sale, without additional consideration by Polaris Venture Partners IV, L.P. (&quot;PVP IV&quot;) and Polaris Venture Partners Entrepreneurs' Fund IV, L.P. (&quot;PVPE IV&quot; and, together with PVP IV, the &quot;Funds&quot;) to their respective limited partners.  In addition, in connection with the above mentioned distribution, each of,  PVP IV distributed 6,850 shares and PVPE IV distributed 130 shares to Polaris Venture Management Co. IV, L.L.C. (&quot;PVM IV&quot;).  The distribution of these 6,980 shares by PVP IV and PVPE IV to PVM IV is an exempt transaction and not reported in column 4 because the transaction merely reflected a change in the beneficial ownership of those shares.</footnote>
        <footnote id="F2">Represents 680,269 shares distributed by PVP IV to its limited partners and 12,751 shares distributed by PVPE IV to its limited partners.</footnote>
        <footnote id="F3">Represents 586,056 shares, 10,102 shares, and 8,975 shares directly owned by PVP IV, PVPE IV and PVM IV, respectively.</footnote>
        <footnote id="F4">The Reporting Person is a managing member of PVM IV, the general partner of each of PVP IV and PVPE IV.  The Reporting Person 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>
        <footnote id="F5">Represents a pro rata distribution, and not a purchase or sale, without additional consideration by PVM IV to its members and assignees.</footnote>
        <footnote id="F6">Represents 586,056 shares, 10,102 shares, and 1,995 shares directly owned by PVP IV, PVPE IV and PVM IV, respectively.</footnote>
    </footnotes>

    <remarks>Exhibit 24 - Power of Attorney</remarks>

    <ownerSignature>
        <signatureName>/s/ Mary Blair, Attorney in-Fact for Terrance McGuire</signatureName>
        <signatureDate>2016-11-21</signatureDate>
    </ownerSignature>
</ownershipDocument>
