To provide an air-conditioner which is improved especially in cooling capacity by annexing an auxiliary heat-exchanger to an outdoor heat-exchanger.

An auxiliary heat-exchanger 6 and a first on-off valve 7 are interconnected in series, in the order, between a four-way valve 2 and an outdoor heat-exchanger 3 and situated in the vicinity of the outdoor heat-exchanger. A bypass passage 8 having a second on-off valve 9 is connected to a section between the four-way valve and the auxiliary heat-exchanger and a section between the first on-off valve and the outdoor heat-exchanger. During cooling operation, the first on-off valve is opened and the second on-off valve is closed and the auxiliary heat-exchanger forms a condenser. During heating operation, the first on-off valve is closed and the second on-off valve is opened, and a refrigerant bypasses the auxiliary heat-exchanger through the bypass passage.