An air conditioning system for a vehicle has a cool storage heat exchanger for continuing cooling operation with stored cooling energy during a compressor is stopped due to a temporal stop of an engine for the vehicle. Cooling energy is stored in the cool storage material of the cool storage heat exchanger during a normal cooling operation during which the compressor is operated by the engine. When the vehicle stops, for example before a traffic lamp, and thereby the compressor is not operated, an ejector is operated to circulate the refrigerant from the cool storage heat exchanger to an evaporator so that the cooling operation can be continued.