The amount of secondary air flowing through a bypass air passage bypassing the throttle valve of an engine, which is connected to an automatic transmission of a vehicle having an air-conditioner, is controlled by an air control valve disposed in the bypass air passage. The air control valve is controlled on the basis of the result of comparison between a signal indicative of the actual idling rotation speed of the engine detected by the distributor of the engine and a reference signal indicative of a desired idling rotation speed of the engine. The level of this reference signal indicative of the desired idling rotation speed of the engine varies depending on the on-off of the air-conditioner in the vehicle or on the position of the shift lever of the automatic transmission.
