A vehicle air-conditioning apparatus comprising: a hot water heater core provided in a hot water circuit in which cooling water circulates in a heat source to recover waste heat of the heat source, and configured to exchange heat between the cooling water heated by the waste heat of the heat source and air to heat the air, thereby heating an inside of a vehicle by using the heated air; a heat pump configured to exchange heat between a refrigerant discharged from a refrigerant compressor and air by using an indoor heat exchanger to heat the air, thereby heating the inside of the vehicle by using the heated air; an electric heater configured to heat air to heat the inside of the vehicle; and a controller configured to select at least one of the hot water heater core, the heat pump and the electric heater to perform heating, characterized in that the controller is configured to use, when a temperature of the cooling water heated by the waste heat of the heat source is equal to or greater than a predetermined threshold, the hot water heater core as a main heat source for heating; the controller is configured to, when the hot water heater core is used as the main heat source for heating, operate the hot water heater core, the heat pump and the electric heater by allocating a required determined heating capacity to the hot water heater core, the heat pump and the electric heater in this order in such a manner that, if the required determined heating capacity can be covered with the hot water heater core, only the hot water heater core is used, and if not, the heat pump is used to cover a shortage, and if the heat pump still cannot cover the shortage, the electric heater is used to cover the shortage; wherein the controller is configured to, if a temperature of the cooling water heated by the waste heat of the heat source is less than a predetermined threshold, use the heat pump as a main heat source for heating and to set a prohibition time; said prohibition time being a time period during which a heating operation using the hot water heater core is prevented. a hot water heater core provided in a hot water circuit in which cooling water circulates in a heat source to recover waste heat of the heat source, and configured to exchange heat between the cooling water heated by the waste heat of the heat source and air to heat the air, thereby heating an inside of a vehicle by using the heated air; a heat pump configured to exchange heat between a refrigerant discharged from a refrigerant compressor and air by using an indoor heat exchanger to heat the air, thereby heating the inside of the vehicle by using the heated air; an electric heater configured to heat air to heat the inside of the vehicle; and a controller configured to select at least one of the hot water heater core, the heat pump and the electric heater to perform heating, characterized in that the controller is configured to use, when a temperature of the cooling water heated by the waste heat of the heat source is equal to or greater than a predetermined threshold, the hot water heater core as a main heat source for heating; the controller is configured to, when the hot water heater core is used as the main heat source for heating, operate the hot water heater core, the heat pump and the electric heater by allocating a required determined heating capacity to the hot water heater core, the heat pump and the electric heater in this order in such a manner that, if the required determined heating capacity can be covered with the hot water heater core, only the hot water heater core is used, and if not, the heat pump is used to cover a shortage, and if the heat pump still cannot cover the shortage, the electric heater is used to cover the shortage; the controller is configured to, if a temperature of the cooling water heated by the waste heat of the heat source is less than a predetermined threshold, use the heat pump as a main heat source for heating and to set a prohibition time; said prohibition time being a time period during which a heating operation using the hot water heater core is prevented.