A gas turbine combustor forms a combustion region R1 therein by burning a premixed gas obtained by previously mixing a fuel and combustion air. The gas turbine combustor includes: a burner cylinder (51) in which the premixed gas passes; a film air supply port (61) that is provided on the burner cylinder 51, and supplies a film air formed into a film shape and flowing along the inner wall surface (the inner circumferential surface) of the burner cylinder (51); and a cooling passage (71) in which a cooling air passes. The cooling air cools a back-step surface (65) facing the formed combustion region R1. The cooling passage (71) includes a side from which the cooling air flows out, and the side is connected to the film air supply port (61).