A control device for a vehicle is provided. The vehicle includes an engine, an accessory, a continuously variable transmission, and a lock-up clutch. The control device includes an electronic control unit. The electronic control unit is configured to: when the load state is less than a predetermined value, control the speed ratio of the continuously variable transmission and the rotational speed of the engine such that the rotational speed of the engine during engagement of the lock-up clutch is kept at a first rotational speed; and when the load state is greater than or equal to the predetermined value, control the speed ratio of the continuously variable transmission and the rotational speed of the engine such that the rotational speed of the engine during engagement of the lock-up clutch becomes a second rotational speed higher than the first rotational speed.