A control system for an accessory of an automobile includes an engine output detector for detecting the output of the engine of the automobile, a gear transmissioon coupled to the engine and responsive to detection of an idling condition of the automboile for selecting a neutral gear position, an accessory such as an air conditioner compressor drivable by the engine, a clutch disposed between the accessory and the engine for applying and cutting off the output of the engine to the accessory, a speed sensor for detecting the speed of travel of the automobile, a control circuit for comparing an actual running condition of the automobile with a prescribed running condition in which the output of the engine and the speed of the automobile are lower than respective prescribed levels, and for inhibiting operation of the accessory by disconnecting the clutch when the automobile is under the prescribed running condition.