An air-conditioner for a vehicle includes: a heater core which heats air for air-conditioning by using cooling water of a cooling circuit which cools a fuel cell of a fuel cell vehicle or an engine of a hybrid car as a heat source; a heat exchanger arranged upstream of the heater core in a flow of the air for air-conditioning to heat the air for air-conditioning by using refrigerant which flows through a heat pump cycle as a heat source; and a control part which controls operation of the heat pump cycle in a manner that a target temperature of the air for air-conditioning heated by the heat exchanger is changed in accordance with a temperature of the cooling water.