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

    <schemaVersion>X0306</schemaVersion>

    <documentType>5/A</documentType>

    <periodOfReport>2012-07-31</periodOfReport>

    <dateOfOriginalSubmission>2012-09-13</dateOfOriginalSubmission>

    <notSubjectToSection16>0</notSubjectToSection16>

    <form3HoldingsReported>0</form3HoldingsReported>

    <form4TransactionsReported>0</form4TransactionsReported>

    <issuer>
        <issuerCik>0000827773</issuerCik>
        <issuerName>PUTNAM PREMIER INCOME TRUST</issuerName>
        <issuerTradingSymbol>PPT</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001198272</rptOwnerCik>
            <rptOwnerName>CURTIS B CHARLES</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O PUTNAM LLC</rptOwnerStreet1>
            <rptOwnerStreet2>ONE POST OFFICE SQUARE L5</rptOwnerStreet2>
            <rptOwnerCity>BOSTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02109</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Putnam Premier Income Trust</value>
            </securityTitle>
            <transactionDate>
                <value>2012-07-31</value>
                <footnoteId id="F1"/>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>5</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>28.154</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>5.63</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>388.688</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Dividends reinvested for fiscal year end 2012.</footnote>
        <footnote id="F2">Price as of July 31, 2012</footnote>
    </footnotes>

    <remarks>This amendment is being filed in relation to two prior Form 5 filings for Mr. Curtis with respect to his holdings in Putnam Premier Income Trust as of the fund's most recent fiscal year end.  The second of those two filings (SEC accession number 0001389055-12-000008) contained the correct information, while the prior filing (SEC accession number 0001389055-12-000006) did not.  Both such filings were made as Form 5 filings.  This filing replicates the information included in the second filing, but is filed as a Form 5/A to indicate that it amends the prior filing.</remarks>

    <ownerSignature>
        <signatureName>/s/ Charles B. Curtis</signatureName>
        <signatureDate>2012-10-11</signatureDate>
    </ownerSignature>
</ownershipDocument>
