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

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2011-06-03</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000216039</issuerCik>
        <issuerName>GRUBB &amp; ELLIS CO</issuerName>
        <issuerTradingSymbol>GBE</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001504537</rptOwnerCik>
            <rptOwnerName>Streiff Mathieu B.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O GRUBB &amp; ELLIS COMPANY</rptOwnerStreet1>
            <rptOwnerStreet2>1551 N. TUSTIN AVENUE, SUITE 300</rptOwnerStreet2>
            <rptOwnerCity>SANTA ANA</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>92705</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>EVP/General Counsel/Secretary</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $0.01</value>
            </securityTitle>
            <transactionDate>
                <value>2011-06-03</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>13894</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.60</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>89281</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>11.36</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <value>2017-01-23</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, par value $0.01</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>10560</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>10560</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Represents 13,894 restricted shares of common stock of Grubb &amp; Ellis Company (the &quot;Company&quot;) that were withheld upon vesting to satisfy Mr. Streiff's tax withholding obligation in connection with the vesting of a total of 33,333 restricted shares of the Company's common stock that were previously awarded to Mr. Streiff.</footnote>
        <footnote id="F2">On June 2, 2011, the effective date for determination of tax withholding requirements related to Mr. Streiff's vested restricted shares of the Company's common stock, the closing price for the Company's common stock was $0.60.</footnote>
        <footnote id="F3">Beneficially owned shares include (i) 55,948 shares of the Company's common stock, with 19,439 of such shares representing the balance of the 33,333 restricted shares that vested on June 3, 2011 minus the 13,894 shares that were withheld to satisfy Mr. Streiff's tax withholding obligation and (ii) 33,333 restricted shares of the Company's common stock that were granted to Mr. Streiff on June 3, 2009 pursuant to the Company's 2006 Omnibus Equity Plan and which will vest on the third anniversary of the grant date.</footnote>
        <footnote id="F4">The stock option was issued to Mr. Streiff on January 23, 2007. The stock option has fully vested and is exercisable at any time until January 23, 2017, with respect to Mr. Streiff's option to purchase 10,560 shares of the Company's common stock at $11.36 per share.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Mathieu B. Streiff</signatureName>
        <signatureDate>2011-06-13</signatureDate>
    </ownerSignature>
</ownershipDocument>
