In a control device for a vehicle including: a dog clutch mechanism that is disposed in a power transmission path in which a driving force is transmitted from an engine to a wheel and is operated by a hydraulic actuator; and an electric oil pump that supplies hydraulic pressure to the hydraulic actuator, rotation of the engine is stopped in a state in which the dog clutch mechanism is engaged by the hydraulic pressure supplied from the electric oil pump at a time during an engine stop operation, the rotation of the engine is started in the state in which the dog clutch mechanism is engaged by the hydraulic pressure supplied from the electric oil pump at a time during an engine restart operation, hence occurrence of up-lock of the dog clutch mechanism is prevented.