A gas turbine combustor having a combustion chamber (10) with a steam-cooled peripheral wall (2) has an air hole (1) for injecting dilution air therethrough bored in the peripheral wall (2) on an upstream side of the combustion chamber (10). The air is thereby supplied through the air hole (1) into the vicinity of an inner surface of the peripheral wall (2) to form a film flow of air, and an increase of the fuel concentration there is suppressed. The dilution air is preferably supplied from a gas turbine compressor (6).
