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

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2011-03-10</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001371918</rptOwnerCik>
            <rptOwnerName>Hanson Jeffrey T</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>Chief Investment Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $0.01</value>
            </securityTitle>
            <transactionDate>
                <value>2011-03-10</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>63379</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>1.01</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1156763</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>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Jeffrey T. Hanson &amp; April L. Hanson, Trustees of the Hanson Family Trust</value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>10.00</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F7"/>
            </exerciseDate>
            <expirationDate>
                <value>2016-11-16</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, par value $0.01</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>22000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>22000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Represents 63,379 restricted shares of common stock of Grubb &amp; Ellis Company (the &quot;Company&quot;) that were withheld upon vesting to satisfy Mr. Hanson's tax withholding obligation in connection with the vesting of a total of 166,667 restricted shares of the Company's common stock that were previously awarded to Mr. Hanson.</footnote>
        <footnote id="F2">On March 9, 2011, the effective date for determination of tax withholding requirements related to Mr. Hanson's vested restricted shares of the Company's common stock, the closing price for the Company's common stock was $1.01</footnote>
        <footnote id="F3">Beneficially owned shares include 1,000,000 restricted shares of the Company's common stock granted to Mr. Hanson pursuant to the Company's 2006 Omnibus Equity Plan, (A) 500,000 of which are subject to vesting over 3 years in equal annual increments of 1/3 each, commencing on the 1 year anniversary of the grant date (March 10, 2010) 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. Vesting with respect to all 1,000,000 restricted shares is subject to Mr. Hanson's continued employment by the Company and subject to the terms of a restricted share agreement entered into by Mr. Hanson and the Company.</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. Hanson's option and has no expiration date.</footnote>
        <footnote id="F7">The option has become fully exercisable as of November 16, 2008.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Jeffrey T. Hanson</signatureName>
        <signatureDate>2011-03-14</signatureDate>
    </ownerSignature>
</ownershipDocument>
