A thermal storage air conditioner comprising: 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, wherein the securing member of the thermal storage unit includes a bracket for partially surrounding and holding the thermal storage heat exchanger, and holding hooks for securing opposite ends of the bracket to insides of the thermal storage tank, respectively, wherein the thermal storage heat exchanger further includes frozen amount measuring means for measuring an extent of freeze done by the thermal storage heat exchanger, and wherein the frozen amount measuring means is attached to the securing member which secures the thermal storage heat exchanger, for measuring an extent of freeze done by the thermal storage heat exchanger based on deformation of the securing member caused by phase change of the thermal storage substance in the thermal storage tank. 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, wherein the securing member of the thermal storage unit includes a bracket for partially surrounding and holding the thermal storage heat exchanger, and holding hooks for securing opposite ends of the bracket to insides of the thermal storage tank, respectively, wherein the thermal storage heat exchanger further includes frozen amount measuring means for measuring an extent of freeze done by the thermal storage heat exchanger, and wherein the frozen amount measuring means is attached to the securing member which secures the thermal storage heat exchanger, for measuring an extent of freeze done by the thermal storage heat exchanger based on deformation of the securing member caused by phase change of the thermal storage substance in the thermal storage tank.