A narrow gap laser-TIG arc hybrid welding apparatus and welding method. The welding apparatus comprises a welding gun body (14), a swing welding gun assembly, a welding wire feeding and heating assembly, and a gas conveying assembly; the swing welding gun assembly comprises a welding gun rotating shaft (1), a stepper motor (6), a large gear (3), a small gear (2), an upper insulating sleeve (4), a lower insulating sleeve (22), a tungsten electrode clamp (24), and a tungsten electrode (25); the stepper motor (6) is mounted on a motor connection seat (7); the small gear (2) is mounted on the output shaft of the stepper motor (6); the large gear (3) is mounted on the welding gun rotating shaft (1); the small gear (2) is engaged with the large gear (3); the welding gun rotating shaft (1) is mounted and positioned on the welding gun body (14) by means of the upper insulating sleeve (4) and the lower insulating sleeve (22); the tungsten electrode (25) is mounted at the tail end of the welding gun rotating shaft (1) by means of the tungsten electrode clamp (24); the welding wire feeding and heating assembly feeds a wire and heats same; the focus point of welding arc and a laser beam together act on a same welding pool region; the gas conveying assembly conveys protective welding gas to a welding arc region.