To ensure air conditioning performance of an air conditioner during off-road running of a vehicle.

A compressor 20 of the air conditioner 18 is connected to an engine 11 via an electromagnetic clutch 19. Whether a vehicle is rapidly accelerated or not is determined based on an accelerator operation amount and the like. When the vehicle is determined to be in the rapid acceleration, an air conditioner cut on acceleration is carried out that stops the drive of the compressor 20 by changing over the electromagnetic clutch 19 to a power cutoff state. Furthermore, whether the vehicle is in off-road running or not is determined based on a differential gear changeover switch 23, a vehicle height adjustment switch 25, road-surface select switch 26, etc. When the off-road running is determined, the drive of the compressor 20 is continued during the off-road running even on the acceleration by prohibiting the air conditioner cut on acceleration. Thereby, the air conditioning performance of the air conditioner 18 is ensured during the off-road running and uncomfortable torque shock is prevented by inhibiting the fluctuation of output torque by the stop of the drive of the compressor 20.