The invention provides an air conditioner system which comprises a compressor, a first heat exchanger, a second heat exchanger, a control device and an energy storage device. The air conditioner system has a first operation mode, a second operation mode and a third operation mode through switching of the control device. Under the first operation mode, the amount of refrigerants sucked in from an air suction opening of the compressor is equal to the amount of refrigerants output from a high-pressure storage tank; under the second operation mode, the amount of refrigerants output from the high-pressure storage tank is smaller than the amount of refrigerants sucked in from the air suction opening of the compressor, and part of refrigerants discharged by the compressor is stored in the high-pressure storage tank; and under the third operation mode, the compressor stops operating, and the refrigerants stored in the high-pressure storage tank is used for refrigerating or heating of the air conditioner system. The invention further provides a control method of the air conditioner system. According to the air conditioner system and the control method thereof, an energy storage function of the air conditioner system is achieved, and the electricity consumption is lowered; and moreover, the energy storage device of the air conditioner system has the advantages of being simple in structure and small in stored energy loss.