A control device of a vehicle includes an engine, an electric motor, and a first clutch connecting/disconnecting a power transmission path between the engine and the electric motor, and a second clutch configured to achieve a mechanically directly-coupled state of a power transmission path between the engine/the electric motor and drive wheels, the control device of a vehicle increasing a torque of the electric motor and causing the second clutch to slip-engage when the engine is started by controlling the first clutch toward engagement during motor running using only the electric motor as a drive force source for running with the first clutch released and the second clutch engaged, when the torque of the electric motor increased at the start of the engine relative to the torque of the electric motor during the motor running is larger, a slip amount of the second clutch being made larger as compared to when the torque is smaller.