A heat pump air-conditioning system for a vehicle includes a refrigerant circuit, an auxiliary heater, and a control unit. The control unit compares a difference between a target blowout temperature and an actual blowout temperature with a predetermined first temperature threshold value in magnitudes, The control unit adjusts an opening degree of a first expansion valve and an opening degree of a second expansion valve. The control unit adjusts an output power of the auxiliary heater. The control unit executes a plurality of different modes of a heat pump air-conditioning to control the actual blowout temperature to approach and maintain at the target blowout temperature.