An air-conditioning apparatus including a compressor, a first heat exchanger, an expansion device, and a second heat exchanger that are connected by a refrigerant pipe to form a refrigeration cycle, the air-conditioning apparatus using a non-azeotropic refrigerant mixture as a refrigerant for the refrigeration cycle, the air-conditioning apparatus comprising: a bypass connected to bypass the compressor; a bypass heat exchanger provided in the bypass and configured to cool the refrigerant flowing from the compressor into the bypass; a second expansion device provided in the bypass and configured to reduce a pressure of the refrigerant cooled by the bypass heat exchanger; refrigerant state detecting means (53 to 55) for detecting a temperature of the refrigerant flowing into the second expansion device, a temperature of the refrigerant flowing out of the second expansion device, and a pressure of the refrigerant sucked into the compressor; and a computing device configured to calculate a composition of the refrigerant circulating in the refrigeration cycle on a basis of a detection result of the refrigerant state detecting means (53 to 55), wherein the computing device calculates a quality of the refrigerant flowing out of the second expansion device on a basis of an inlet liquid enthalpy calculated on a basis of the temperature of the refrigerant flowing into the second expansion device and a saturated gas enthalpy and a saturated liquid enthalpy calculated on a basis of the temperature of the refrigerant flowing out of the second expansion device or the pressure of the refrigerant sucked into the compressor; calculates a liquid-phase concentration and a gas-phase concentration of the refrigerant flowing out of the second expansion device on the basis of the temperature of the refrigerant flowing out of the second expansion device and the pressure of the refrigerant sucked into the compressor; and calculates the composition of the refrigerant circulating in the refrigeration cycle on a basis of the calculated quality, liquid-phase concentration, and gas-phase concentration. a bypass connected to bypass the compressor; a bypass heat exchanger provided in the bypass and configured to cool the refrigerant flowing from the compressor into the bypass; a second expansion device provided in the bypass and configured to reduce a pressure of the refrigerant cooled by the bypass heat exchanger; refrigerant state detecting means (53 to 55) for detecting a temperature of the refrigerant flowing into the second expansion device, a temperature of the refrigerant flowing out of the second expansion device, and a pressure of the refrigerant sucked into the compressor; and a computing device configured to calculate a composition of the refrigerant circulating in the refrigeration cycle on a basis of a detection result of the refrigerant state detecting means (53 to 55), wherein the computing device calculates a quality of the refrigerant flowing out of the second expansion device on a basis of an inlet liquid enthalpy calculated on a basis of the temperature of the refrigerant flowing into the second expansion device and a saturated gas enthalpy and a saturated liquid enthalpy calculated on a basis of the temperature of the refrigerant flowing out of the second expansion device or the pressure of the refrigerant sucked into the compressor; calculates a liquid-phase concentration and a gas-phase concentration of the refrigerant flowing out of the second expansion device on the basis of the temperature of the refrigerant flowing out of the second expansion device and the pressure of the refrigerant sucked into the compressor; and calculates the composition of the refrigerant circulating in the refrigeration cycle on a basis of the calculated quality, liquid-phase concentration, and gas-phase concentration.