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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4/A</documentType>

    <periodOfReport>2018-09-25</periodOfReport>

    <dateOfOriginalSubmission>2018-09-27</dateOfOriginalSubmission>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001534120</issuerCik>
        <issuerName>Cerecor Inc.</issuerName>
        <issuerTradingSymbol>CERC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001754540</rptOwnerCik>
            <rptOwnerName>Crutcher Patrick J</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CERECOR INC.</rptOwnerStreet1>
            <rptOwnerStreet2>400 E. PRATT STREET, SUITE 606</rptOwnerStreet2>
            <rptOwnerCity>BALTIMORE</rptOwnerCity>
            <rptOwnerState>MD</rptOwnerState>
            <rptOwnerZipCode>21202</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>VP, Business Development</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-09-25</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1641642</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1641642</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Received in exchange for 1,000,000 shares of Ichorion Therapeutics, Inc. common stock in connection with the merger of Ichorion Therapeutics, Inc. into the Issuer.  On September 25, 2018 the closing price of the Issuer's common stock was $4.55 per share.</footnote>
    </footnotes>

    <remarks>This Form 4 amendment is being filed to reflect the correct number of shares received in connection with the merger of Ichorion Therapeutics, Inc. into the Issuer.</remarks>

    <ownerSignature>
        <signatureName>/s/ Donald R. Reynolds, by Power of Attorney</signatureName>
        <signatureDate>2018-10-04</signatureDate>
    </ownerSignature>
</ownershipDocument>
