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

    <schemaVersion>X0304</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2011-12-05</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001421694</rptOwnerCik>
            <rptOwnerName>VAN BERKEL JACOB</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 and COO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $0.01</value>
            </securityTitle>
            <transactionDate>
                <value>2011-12-05</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>14672</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.22</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1044770</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Convertible Preferred Stock, par value $0.01</value>
                <footnoteId id="F4"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F5"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F6"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F6"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, par value $0.01</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <footnoteId id="F5"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>250</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Represents 14,672 restricted shares of common stock of Grubb &amp; Ellis Company (the &quot;Company&quot;) that were withheld upon vesting to satisfy Mr. Van Berkel's tax withholding obligation in connection with the vesting of a total of 40,000 restricted shares of the Company's common stock that were previously awarded to Mr. Van Berkel.</footnote>
        <footnote id="F2">On December 2, 2011, the effective date for determination of the tax withholding requirements related to Mr. Van Berkel's vested restricted shares of the Company's common stock, the closing price for the Company's common stock was $0.22.</footnote>
        <footnote id="F3">Beneficially owned shares include (i) 211,437 shares of the Company's common stock, with 25,328 of such shares representing the balance of the 40,000 restricted shares that vested on December 5, 2011 minus the 14,672 shares that were withheld to satisfy Mr. Van Berkel's tax withholding obligation and (ii) 833,333 restricted shares of the Company's common stock that were granted to Mr. Van Berkel on March 10, 2010 pursuant to the Company's 2006 Omnibus Equity Plan, (A) 333,333 of which vest in equal 1/2 portions on each of the second and third anniversaries of the grant date and (B) 500,000 of which are subject to vesting based upon the market price of the Company's common stock during the 3 year period beginning March 10, 2010. All such 833,333 restricted shares are subject to Mr. Van Berkel's continued employment by the Company and to the terms of a restricted share agreement.</footnote>
        <footnote id="F4">The full title of the deriviative security is 12% Cumulative Participating Perpetual Convertible Preferred Stock, par value $0.01 per share (the &quot;Preferred Stock&quot;).</footnote>
        <footnote id="F5">Each share of Preferred Stock is convertible into 60.606 shares of the Company's common stock, which represents a conversion price of approximately $1.65 per share.</footnote>
        <footnote id="F6">The Preferred Stock is convertible, in whole or in part, into common stock at any time at Mr. Van Berkel's option and has no expiration date.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Jacob Van Berkel</signatureName>
        <signatureDate>2011-12-07</signatureDate>
    </ownerSignature>
</ownershipDocument>
