A control device for a vehicle including an engine and an automatic transmission having a variator and a power transmission mechanism , the control device comprising: a control unit configured to execute a sailing-stop control which stops the engine and disengages an engagement element provided in the power transmission mechanism during running of the vehicle, wherein the control unit is configured to give an engagement instruction to the engagement element so that the engagement element is engaged when a rotation speed of the engine becomes a target engine rotation speed set on the basis at least of a vehicle speed and a speed ratio of the variator after the engine is started, if a cancellation request for the sailing-stop control is made during execution of the sailing-stop control, characterized in that the control unit is configured to raise the target engine rotation speed within a range not higher than a rotation speed of a blown-up peak at start of the engine by downshifting the variator before the engagement element is engaged and is configured to give the engagement instruction to the engagement element so that the engagement element is engaged when the engine rotation speed becomes the raised target engine rotation speed, if the target engine rotation speed when the cancellation request for the sailing-stop control is made is less than a first predetermined value. a control unit configured to execute a sailing-stop control which stops the engine and disengages an engagement element provided in the power transmission mechanism during running of the vehicle, wherein the control unit is configured to give an engagement instruction to the engagement element so that the engagement element is engaged when a rotation speed of the engine becomes a target engine rotation speed set on the basis at least of a vehicle speed and a speed ratio of the variator after the engine is started, if a cancellation request for the sailing-stop control is made during execution of the sailing-stop control, characterized in that the control unit is configured to raise the target engine rotation speed within a range not higher than a rotation speed of a blown-up peak at start of the engine by downshifting the variator before the engagement element is engaged and is configured to give the engagement instruction to the engagement element so that the engagement element is engaged when the engine rotation speed becomes the raised target engine rotation speed, if the target engine rotation speed when the cancellation request for the sailing-stop control is made is less than a first predetermined value. the control unit is configured to give an engagement instruction to the engagement element so that the engagement element is engaged when a rotation speed of the engine becomes a target engine rotation speed set on the basis at least of a vehicle speed and a speed ratio of the variator after the engine is started, if a cancellation request for the sailing-stop control is made during execution of the sailing-stop control, characterized in that the control unit is configured to raise the target engine rotation speed within a range not higher than a rotation speed of a blown-up peak at start of the engine by downshifting the variator before the engagement element is engaged and is configured to give the engagement instruction to the engagement element so that the engagement element is engaged when the engine rotation speed becomes the raised target engine rotation speed, if the target engine rotation speed when the cancellation request for the sailing-stop control is made is less than a first predetermined value. <EOS>