Provided is an air-conditioning apparatus for a vehicle based on heat storage and cold storage. The apparatus includes a coolant supply unit supplying a first coolant circulating within a vehicle, a cooling unit repeatedly performing a cooling cycle using a refrigerant circulating though a first flow pipe unit, a hot/cold accumulation unit storing a second coolant of a preset capacity and communicating with the coolant supply unit through second flow pipe units, wherein the temperature of the second coolant is converted into a temperature capable of heating and accumulated in the hot/cold accumulation unit, the evaporator of the cooling unit is disposed within the hot/cold accumulation unit, and the temperature of the second coolant is converted into a temperature capable of cooling and accumulated in the hot/cold accumulation unit during the cooling cycle.