A control device for a vehicle includes an electronic control unit. The electronic control unit is configured to: execute first automatic stop control for automatically stopping an engine when a first condition is established during traveling of the vehicle; execute second stop control for automatically stopping the engine when a second condition is established during stop of the vehicle; predict a vehicle stop duration; calculate a required cold and heat storage amount of an evaporator; calculate a reaching time until a cold and heat storage amount of the evaporator reaches the required cold and heat storage amount; predict a time needed for vehicle stop; and when the first condition is established during traveling of the vehicle, in a case where the calculated reaching time is equal to or longer than the predicted time needed for vehicle stop, automatically stop the internal combustion engine during traveling of the vehicle.