An air-conditioning apparatus comprising a compressor, an indoor heat exchanger, an expansion device, and an outdoor heat exchanger that form a refrigeration cycle circuit through which refrigerant circulates, the outdoor heat exchanger comprising: a plurality of heat-transfer tubes arranged in such a manner as to project therefrom on both sides; a first header connected to one end of each of the plurality of heat-transfer tubes; a second header (10, 10a, 10b) connected to an other end of each of the plurality of heat-transfer tubes; and a plurality of fins joined to each of the plurality of heat-transfer tubes, and the second header (10, 10a, 10b) comprising a plurality of branch tubes and a header manifold, the header manifold of the second header (10, 10a, 10b) having a flow space that communicates with each of the plurality of branch tubes connected to corresponding one of the plurality of heat-transfer tubes, the gas-liquid two-phase refrigerant flowing upward in the flow space and discharging the gas-liquid two-phase refrigerant into the plurality of branch tubes when the outdoor heat exchanger serves as an evaporator; characterised in that a controller is provided configured such that the quality x of the refrigerant flowing into the second header (10, 10a, 10b) falls within the range 0.05 ≤ x ≤ 0.30, so that the refrigerant flowing into the header manifold is configured to form a pattern of annular flow or churn flow; and tips of the branch tubes are inserted into the header manifold so as to pass through a liquid-phase portion having a thickness δ [m] = D/4 and reach a gas-phase portion; wherein the thickness δ [m] of the liquid-phase portion is defined as δ = G×(1-x)×D/(4ρ L ×U LS), where G is a flow speed [kg/(m 2 s)] of the refrigerant, x is a quality of the refrigerant, D is an inside diameter [m] of the header manifold, ρ L is a liquid density [kg/m 3] of the refrigerant, U LS is a reference apparent liquid speed [m/s] that is a maximum value within a range of variation in an apparent liquid speed of the refrigerant flowing into the flow space of the header manifold, the reference apparent liquid speed U LS [m/s] being defined as G(1-x)/ρ L. a compressor, an indoor heat exchanger, an expansion device, and an outdoor heat exchanger that form a refrigeration cycle circuit through which refrigerant circulates, the outdoor heat exchanger comprising: a plurality of heat-transfer tubes arranged in such a manner as to project therefrom on both sides; a first header connected to one end of each of the plurality of heat-transfer tubes; a second header (10, 10a, 10b) connected to an other end of each of the plurality of heat-transfer tubes; and a plurality of fins joined to each of the plurality of heat-transfer tubes, and the second header (10, 10a, 10b) comprising a plurality of branch tubes and a header manifold, the header manifold of the second header (10, 10a, 10b) having a flow space that communicates with each of the plurality of branch tubes connected to corresponding one of the plurality of heat-transfer tubes, the gas-liquid two-phase refrigerant flowing upward in the flow space and discharging the gas-liquid two-phase refrigerant into the plurality of branch tubes when the outdoor heat exchanger serves as an evaporator; characterised in that a controller is provided configured such that the quality x of the refrigerant flowing into the second header (10, 10a, 10b) falls within the range 0.05 ≤ x ≤ 0.30, so that the refrigerant flowing into the header manifold is configured to form a pattern of annular flow or churn flow; and tips of the branch tubes are inserted into the header manifold so as to pass through a liquid-phase portion having a thickness δ [m] = D/4 and reach a gas-phase portion; wherein the thickness δ [m] of the liquid-phase portion is defined as δ = G×(1-x)×D/(4ρ L ×U LS), where G is a flow speed [kg/(m 2 s)] of the refrigerant, x is a quality of the refrigerant, D is an inside diameter [m] of the header manifold, ρ L is a liquid density [kg/m 3] of the refrigerant, U LS is a reference apparent liquid speed [m/s] that is a maximum value within a range of variation in an apparent liquid speed of the refrigerant flowing into the flow space of the header manifold, the reference apparent liquid speed U LS [m/s] being defined as G(1-x)/ρ L.