Thermal storage air conditioner including an outdoor unit having an outdoor heat exchanger for making heat exchange, and at least one compressor for compressing refrigerant, an indoor unit having at least one indoor heat exchanger for making heat exchange, a thermal storage unit having a thermal storage tank for holding thermal storage substance therein, a thermal storage heat exchanger for receiving refrigerant from an outside of the thermal storage unit to heat exchange with the thermal storage substance in the thermal storage tank, and a securing member for securing the thermal storage heat exchanger so as to maintain the thermal storage heat exchanger submerged under the thermal storage substance in the thermal storage tank, and a functional unit for selective control of refrigerant flows among the outdoor unit, the indoor unit and the thermal storage unit according to an operation condition, thereby maintaining the thermal storage heat exchanger in the thermal storage tank securely, to prevent drop of heat exchange efficiency caused by movement of the thermal storage heat exchanger.