An air-conditioning apparatus comprising: a heat source device including a compressor that compresses a heat-source-side refrigerant and a heat-source-side heat exchanger that exchanges heat between outside air and the heat-source-side refrigerant; a relay unit including an intermediate heat exchanger that exchanges heat between the heat-source-side refrigerant and a heat medium, an expansion device that reduces a pressure of the heat-source-side refrigerant, and a pump that pressure-feeds the heat medium; an indoor unit including a use-side heat exchanger that exchanges heat between air in an air-conditioned space and the heat medium; and a controller that controls at least the heat source device and the relay unit, wherein a refrigeration cycle through which the heat-source-side refrigerant circulates is formed by connecting the compressor, the heat-source-side heat exchanger, a heat-source-side refrigerant passage of the intermediate heat exchanger, and the expansion device with a refrigerant pipe, a heat medium circuit through which the heat medium circulates is formed by connecting a heat medium passage of the intermediate heat exchanger, the pump, and the use-side heat exchanger with a pipe, and characterized in that while driving the pump, the controller is configured to detect a rotational speed of the pump and, on a basis of the rotational speed, start a heat-medium introducing operation in which the heat medium is introduced into the heat medium circuit, and an air purging operation in which air that has entered the heat medium circuit is discharged; and wherein the air-conditioning apparatus, further comprises: a heat-medium supply valve provided to the pipe to introduce the heat medium into the heat medium circuit; and an air purge valve provided to the pipe to discharge the air that has entered the heat medium circuit, wherein in the heat-medium introducing operation and the air purging operation performed by the configured controller, the heat medium is automatically introduced into the heat medium circuit through the heat-medium supply valve and the air that has entered the heat medium circuit is discharged to outside through the air purge valve. a heat source device including a compressor that compresses a heat-source-side refrigerant and a heat-source-side heat exchanger that exchanges heat between outside air and the heat-source-side refrigerant; a relay unit including an intermediate heat exchanger that exchanges heat between the heat-source-side refrigerant and a heat medium, an expansion device that reduces a pressure of the heat-source-side refrigerant, and a pump that pressure-feeds the heat medium; an indoor unit including a use-side heat exchanger that exchanges heat between air in an air-conditioned space and the heat medium; and a controller that controls at least the heat source device and the relay unit, wherein a refrigeration cycle through which the heat-source-side refrigerant circulates is formed by connecting the compressor, the heat-source-side heat exchanger, a heat-source-side refrigerant passage of the intermediate heat exchanger, and the expansion device with a refrigerant pipe, a heat medium circuit through which the heat medium circulates is formed by connecting a heat medium passage of the intermediate heat exchanger, the pump, and the use-side heat exchanger with a pipe, and characterized in that while driving the pump, the controller is configured to detect a rotational speed of the pump and, on a basis of the rotational speed, start a heat-medium introducing operation in which the heat medium is introduced into the heat medium circuit, and an air purging operation in which air that has entered the heat medium circuit is discharged; and wherein the air-conditioning apparatus, further comprises: a heat-medium supply valve provided to the pipe to introduce the heat medium into the heat medium circuit; and an air purge valve provided to the pipe to discharge the air that has entered the heat medium circuit, wherein a heat-medium supply valve provided to the pipe to introduce the heat medium into the heat medium circuit; and an air purge valve provided to the pipe to discharge the air that has entered the heat medium circuit, wherein in the heat-medium introducing operation and the air purging operation performed by the configured controller, the heat medium is automatically introduced into the heat medium circuit through the heat-medium supply valve and the air that has entered the heat medium circuit is discharged to outside through the air purge valve.