An air-conditioning apparatus, comprising: at least one intermediate heat exchanger that is configured to exchange heat between a refrigerant under two-phase transition or under a supercritical condition and a heat medium such as water and an antifreezing liquid that is different from said refrigerant; a refrigeration cycle with which a compressor, an outdoor heat exchanger, at least one expansion valve, and a refrigerant side flow path of said intermediate heat exchanger are connected via piping through which said refrigerant flows; a heat medium circulation circuit with which a heat medium side flow path of said intermediate heat exchanger, a pump, and a use side heat exchanger are connected via piping through which said heat medium flows; and a controller that is configured to control drive of said compressor and said pump, wherein said compressor and said outdoor heat exchanger are accommodated in a heat source device, and said use side heat exchanger in an indoor unit, respectively, characterized in that said intermediate heat exchanger and said pump are accommodated in a relay unit, and said controller is configured to perform at least one of the following operations comprising a) the operation to stop said pump after the stop of said compressor when stopping said compressor based on a decrease in air-conditioning load in said use side heat exchanger or an operation stop instruction and b) the operation to start said compressor after said pump is started when starting said compressor based on an increase in air-conditioning load in said use side heat exchanger or operation start instructions while the compressor is stopped. at least one intermediate heat exchanger that is configured to exchange heat between a refrigerant under two-phase transition or under a supercritical condition and a heat medium such as water and an antifreezing liquid that is different from said refrigerant; a refrigeration cycle with which a compressor, an outdoor heat exchanger, at least one expansion valve, and a refrigerant side flow path of said intermediate heat exchanger are connected via piping through which said refrigerant flows; a heat medium circulation circuit with which a heat medium side flow path of said intermediate heat exchanger, a pump, and a use side heat exchanger are connected via piping through which said heat medium flows; and a controller that is configured to control drive of said compressor and said pump, wherein said compressor and said outdoor heat exchanger are accommodated in a heat source device, and said use side heat exchanger in an indoor unit, respectively, characterized in that said intermediate heat exchanger and said pump are accommodated in a relay unit, and said controller is configured to perform at least one of the following operations comprising a) the operation to stop said pump after the stop of said compressor when stopping said compressor based on a decrease in air-conditioning load in said use side heat exchanger or an operation stop instruction and b) the operation to start said compressor after said pump is started when starting said compressor based on an increase in air-conditioning load in said use side heat exchanger or operation start instructions while the compressor is stopped. a) the operation to stop said pump after the stop of said compressor when stopping said compressor based on a decrease in air-conditioning load in said use side heat exchanger or an operation stop instruction and b) the operation to start said compressor after said pump is started when starting said compressor based on an increase in air-conditioning load in said use side heat exchanger or operation start instructions while the compressor is stopped.