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

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2010-03-17</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001443387</issuerCik>
        <issuerName>RMR Real Estate Income Fund</issuerName>
        <issuerTradingSymbol>RIF</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>President 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>2010-03-17</value>
            </transactionDate>
            <deemedExecutionDate>
                <value>2010-03-17</value>
            </deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>752</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>24.9030</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1982</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Shares of Beneficial Interest</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>7049.990</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The purchases reported in this Form 4 were made pursuant to a Rule 10b5-1 trading plan established by the reporting person on February 26, 2010.</footnote>
        <footnote id="F2">The price reported in Column 4 is a weighted average price.  The shares were purchased in multiple transactions at prices ranging from $24.877 to $25.000. The reporting person undertakes to provide to RMR Real Estate Income Fund, any security holder of RMR Real Estate Income Fund, or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares purchased at each separate price within the ranges set forth in this footnote to this Form 4.</footnote>
        <footnote id="F3">By RMR Advisors, Inc., of which Mr. Portnoy is Director, President and Owner. 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/ Karen Jacoppo-Wood, Attorney-in-Fact</signatureName>
        <signatureDate>2010-03-19</signatureDate>
    </ownerSignature>
</ownershipDocument>
