An air conditioner having a refrigerating cycle in which a refrigerant flows through a compressor, a four-way valve, an indoor heat exchanger, an expansion valve, an outdoor heat exchanger, and the four-way valve in this order during heating, the air conditioner also having a heat storage tank that accommodates a heat storage material for storing therein heat generated by the compressor and a heat storage heat exchanger, and a heat storage bypass circuit provided to connect a refrigerant pipe between the indoor heat exchanger and the expansion valve and a refrigerant pipe between the four-way valve and an inlet port defined in the compressor, characterized in that - a defrosting bypass circuit is provided to connect a refrigerant pipe between the expansion valve and the outdoor heat exchanger and a refrigerant pipe between an outlet port defined in the compressor and the four-way valve, - an indoor heat exchanger temperature sensor is provided for detecting a temperature in the indoor heat exchanger, an indoor fan for conveying air to the indoor heat exchanger, a heat storage two-way valve provided in the heat storage bypass circuit, and - a controller is provided and configured for providing a normal heating mode and a quick heating mode, in which a warm wind is blown out more quickly than in the normal heating mode, if the indoor heat exchanger temperature sensor detects, in the normal heating mode, a predetermined heating initiation temperature, initiating an operation of the indoor fan, and if the indoor heat exchanger temperature sensor detects, in the quick heating mode, a temperature higher than the predetermined heating initiation temperature, initiating an operation of the indoor fan, and limiting a speed of the indoor fan at a start of operation thereof in the quick heating mode. - a defrosting bypass circuit is provided to connect a refrigerant pipe between the expansion valve and the outdoor heat exchanger and a refrigerant pipe between an outlet port defined in the compressor and the four-way valve, - an indoor heat exchanger temperature sensor is provided for detecting a temperature in the indoor heat exchanger, an indoor fan for conveying air to the indoor heat exchanger, a heat storage two-way valve provided in the heat storage bypass circuit, and - a controller is provided and configured for providing a normal heating mode and a quick heating mode, in which a warm wind is blown out more quickly than in the normal heating mode, if the indoor heat exchanger temperature sensor detects, in the normal heating mode, a predetermined heating initiation temperature, initiating an operation of the indoor fan, and if the indoor heat exchanger temperature sensor detects, in the quick heating mode, a temperature higher than the predetermined heating initiation temperature, initiating an operation of the indoor fan, and limiting a speed of the indoor fan at a start of operation thereof in the quick heating mode. providing a normal heating mode and a quick heating mode, in which a warm wind is blown out more quickly than in the normal heating mode, if the indoor heat exchanger temperature sensor detects, in the normal heating mode, a predetermined heating initiation temperature, initiating an operation of the indoor fan, and if the indoor heat exchanger temperature sensor detects, in the quick heating mode, a temperature higher than the predetermined heating initiation temperature, initiating an operation of the indoor fan, and limiting a speed of the indoor fan at a start of operation thereof in the quick heating mode.