The invention relates to the technical field of air-conditioning and discloses a heat storage defrosting air-conditioning system. The heat storage defrosting air-conditioning system comprises a refrigerant loop and further comprises a first heat storage device and a second heat storage device. A compressor, an indoor heat exchanger, a throttling device, an outdoor heat exchanger and a reversing valve which is used for changing the flow direction of refrigerant are disposed on the refrigerant loop; first heat exchange pipes are disposed in the first heat storage device; second heat exchange pipes are disposed in the second heat storage device; the first heat exchange pipes are in parallel connection with the indoor heat exchanger; the second heat exchange pipes are in parallel connection with a refrigerant pipeline arranged between the reversing valve and the indoor heat exchanger; and the first heat exchange pipes, the second heat exchange pipes and the indoor heat exchanger are selectively connected into the refrigerant loop. According to the heat storage defrosting air-conditioning system, indoor heat is not utilized, the stored heat amount is large, the defrosting time is short, the defrosting effect is good, and the stability of an indoor temperature field and heat comfort of a human body can be improved. The invention further provides a control method of the heat storage defrosting air-conditioning system.