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

    <schemaVersion>X0304</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2012-01-20</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001443387</issuerCik>
        <issuerName>Old RMR Real Estate Income Fund</issuerName>
        <issuerTradingSymbol>RIF</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001243971</rptOwnerCik>
            <rptOwnerName>KOUMANTZELIS ARTHUR G</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>TWO NEWTON PLACE</rptOwnerStreet1>
            <rptOwnerStreet2>255 WASHINGTON STREET, SUITE 300</rptOwnerStreet2>
            <rptOwnerCity>NEWTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02458</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Shares of Beneficial Interest</value>
            </securityTitle>
            <transactionDate>
                <value>2012-01-20</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>120.0852</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">On January 20, 2012, Old RMR Real Estate Income Fund (&quot;Old RIF&quot;) merged with and into RMR Real Estate Income Fund (&quot;RIF&quot;). In the merger, Old RIF shareholders received newly issued common shares and auction preferred shares from RIF in exchange for Old RIF common shares and auction preferred shares, as applicable. In connection with this merger, Mr. Koumantzelis acquired an amount of RIF common shares with an aggregate net asset value equal to the aggregate net asset value of the Old RIF common shares owned by Mr. Koumantzelis on January 20, 2012, and Mr. Koumantzelis's Old RIF common shares were cancelled on the books of Old RIF and became null and void.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ Karen Jacoppo-Wood, as Attorney-in-Fact</signatureName>
        <signatureDate>2012-01-24</signatureDate>
    </ownerSignature>
</ownershipDocument>
