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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-12-30</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0001279704</issuerCik>
        <issuerName>Cellectar Biosciences, Inc.</issuerName>
        <issuerTradingSymbol>CLRB</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001535264</rptOwnerCik>
            <rptOwnerName>AWM Investment Company, Inc.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>527 MADISON AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 2600</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10022</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-12-30</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>64747</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.6873</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>35253</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Limited Partnerships</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-12-31</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>35253</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.6955</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Limited Partnerships</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">This is a weighted average price.</footnote>
        <footnote id="F2">AWM Investment Company, Inc., a Delaware corporation (AWM), is the investment adviser to Special Situations Fund III QP, L.P. (SSFQP), Special Situations Cayman Fund, L.P. (CAYMAN) and Special Situations Life Sciences Fund, L.P. (SSLS and together with SSFQP and CAYMAN, the Funds).  As the investment adviser to the Funds, AWM holds sole voting and investment power over 0 shares of Common Stock of the Issuer (the Shares) held by SSFQP, 0 Shares held by CAYMAN and 0 Shares held by SSLS.</footnote>
        <footnote id="F3">Austin W. Marxe (Marxe), David M. Greenhouse (Greenhouse) and Adam C. Stettner (Stettner) are the controlling principals of AWM.
The reporting person disclaims beneficial ownership of the Shares, except to the extent of its pecuniary interest therein. This report shall not
be deemed an admission that the reporting person is the beneficial owner of the securities reported herein for purposes of Section 16 of the
Securities Exchange Act of 1934, as amended, or for any other purpose.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>Adam C. Stettner</signatureName>
        <signatureDate>2016-01-04</signatureDate>
    </ownerSignature>
</ownershipDocument>
