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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4/A</documentType>

    <periodOfReport>2015-06-01</periodOfReport>

    <dateOfOriginalSubmission>2015-06-03</dateOfOriginalSubmission>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000811808</issuerCik>
        <issuerName>SUMMIT FINANCIAL GROUP INC</issuerName>
        <issuerTradingSymbol>SMMF</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001486521</rptOwnerCik>
            <rptOwnerName>George Georgette R.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>PO BOX 8523</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>CHARLESTON</rptOwnerCity>
            <rptOwnerState>WV</rptOwnerState>
            <rptOwnerZipCode>25303</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-06-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>X</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>2428</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>9.75</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>44607</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>by 401(k) Plan FBO Spouse</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-06-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>X</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1047</value>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>9.75</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>19228</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Sellaro Enterprises, Inc.</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Subscription Rights (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>9.95</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2015-06-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>X</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>42179</value>
                    <footnoteId id="F3"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2015-04-10</value>
            </exerciseDate>
            <expirationDate>
                <value>2015-05-29</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2248</value>
                    <footnoteId id="F3"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Spouse 401(k)</value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Subscription Rights (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>9.95</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2015-06-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>X</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>18181</value>
                    <footnoteId id="F4"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2015-04-10</value>
            </exerciseDate>
            <expirationDate>
                <value>2015-05-29</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1047</value>
                    <footnoteId id="F4"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Sellaro Enterprises, Inc.</value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">On June 3, 2015, the reporting person filed a Form 4 reporting the acquisition of 2,692 shares of common stock. The correct number of shares of common stock acquired was 2,428.  As of June 1, 2015, the amount of securities beneficially owned following the reported transaction was 44,607 shares of common stock.</footnote>
        <footnote id="F2">The reporting person inadvertently omitted reporting on her original Form 4 the acquision of 1,047 shares by a company controlled by the reporting person's spouse.</footnote>
        <footnote id="F3">On June 3, 2015, the reporting person filed a Form 4 reporting the exercise of 2,692 subscription rights to buy common stock.  The correct number of subscription rights exercised was 42,179.  The reporting person also reported the acquisition of 2,692 shares of common stock. The correct number of shares of common stock acquired was 2,248.</footnote>
        <footnote id="F4">The reporting person inadvertently omitted reporting the exercise of 18,181 subscription rights to buy common stock by a company controlled by her spouse resulting in the acquisition of 1,047 shares of common stock.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Teresa D. Ely, Lmtd POA Attorney-in-Fact</signatureName>
        <signatureDate>2015-07-23</signatureDate>
    </ownerSignature>
</ownershipDocument>
