An air-conditioning apparatus comprising: a heat source device having a compressor that pressurizes a primary refrigerant used by changing states between a gas phase and a liquid phase or between a supercritical state and a non-supercritical state, a switching device that switches the circulation direction of said primary refrigerant, and a first heat exchanger connected to said switching device and is installed outside of a building having a plurality of floors or a space leading to the outside; a relay unit having a second heat exchanger that is configured to be disposed on an installed floor different from said heat source device and in a space not to be air-conditioned different from the space to be air-conditioned where the air for cooling or the air for heating is supplied and exchanges heat between said primary refrigerant and a secondary refrigerant mainly composed of water or brine and a pump that conveys said secondary refrigerant; an indoor unit having a third heat exchanger that exchanges heat between said secondary refrigerant and the air in said space to be air-conditioned; a first pipeline that connects said heat source device and said relay unit and through which said first refrigerant flows; and a second pipeline that connects said relay unit and said indoor unit to each other from outside a wall dividing inside and outside of said space to be air-conditioned and that is constituted by at least a set of two and through which said secondary refrigerant in a liquid phase flows, characterized in that said relay unit including a plurality of second heat exchangers performs heating of said secondary refrigerant by at least one of said second heat exchangers and cooling of said secondary refrigerant by at least one of the other second heat exchangers at the same time, and the air-conditioning apparatus performs cooling and heating operations at the same time, by flowing said heated secondary refrigerant into said third heat exchanger of said indoor unit which performs heating and by flowing said cooled secondary refrigerant into said third heat exchanger of said indoor unit which performs cooling. a heat source device having a compressor that pressurizes a primary refrigerant used by changing states between a gas phase and a liquid phase or between a supercritical state and a non-supercritical state, a switching device that switches the circulation direction of said primary refrigerant, and a first heat exchanger connected to said switching device and is installed outside of a building having a plurality of floors or a space leading to the outside; a relay unit having a second heat exchanger that is configured to be disposed on an installed floor different from said heat source device and in a space not to be air-conditioned different from the space to be air-conditioned where the air for cooling or the air for heating is supplied and exchanges heat between said primary refrigerant and a secondary refrigerant mainly composed of water or brine and a pump that conveys said secondary refrigerant; an indoor unit having a third heat exchanger that exchanges heat between said secondary refrigerant and the air in said space to be air-conditioned; a first pipeline that connects said heat source device and said relay unit and through which said first refrigerant flows; and a second pipeline that connects said relay unit and said indoor unit to each other from outside a wall dividing inside and outside of said space to be air-conditioned and that is constituted by at least a set of two and through which said secondary refrigerant in a liquid phase flows, characterized in that said relay unit including a plurality of second heat exchangers performs heating of said secondary refrigerant by at least one of said second heat exchangers and cooling of said secondary refrigerant by at least one of the other second heat exchangers at the same time, and the air-conditioning apparatus performs cooling and heating operations at the same time, by flowing said heated secondary refrigerant into said third heat exchanger of said indoor unit which performs heating and by flowing said cooled secondary refrigerant into said third heat exchanger of said indoor unit which performs cooling.