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

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2009-06-23</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001308438</issuerCik>
        <issuerName>RMR Preferred Dividend Fund</issuerName>
        <issuerTradingSymbol>RDR</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001273871</rptOwnerCik>
            <rptOwnerName>PORTNOY ADAM</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O RMR ADVISORS, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>400 CENTRE STREET</rptOwnerStreet2>
            <rptOwnerCity>NEWTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02458</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle>Pres. of Fund</officerTitle>
            <otherText>Dir., Pres. &amp; Owner of Advisor</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Shares of  Beneficial Interest</value>
            </securityTitle>
            <transactionDate>
                <value>2009-06-23</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>7823.055</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">On June 23, 2009, RDR reorganized with RMR Real Estate Income Fund (&quot;RIF&quot;). In this reorganization the assets of RDR were transferred to, and the liabilities of RDR were assumed by, RIF in exchange for common shares and auction preferred shares of RIF. In connection with this reorganization, Mr. Portnoy acquired an amount of RIF common shares with an aggregate net asset value equal to the aggregate net asset value of the RDR common shares owned by Mr. Portnoy on June 23, 2009, and Mr. Portnoy's RDR common shares were cancelled on the books of RDR and became null and void.</footnote>
        <footnote id="F2">By RMR Advisors, Inc., of which Mr. Portnoy is Director, President and a shareholder. Mr. Portnoy disclaims beneficial ownership of such securities, except to the extent that he may have a pecuniary interest therein.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ Mark Kleifges, attorney-in-fact</signatureName>
        <signatureDate>2009-06-24</signatureDate>
    </ownerSignature>
</ownershipDocument>
