<p>In gas turbine combustor constructed by combustion chamber (10) and steam-cooled peripheral wall (2) thereof, there is bored air hole (1) for injecting dilution air therethrough in the peripheral wall (2) on upstream side of the combustion chamber (10), thereby the air is supplied through the air hole (1) into the vicinity of inner surface of the peripheral wall (2) to form film flow of air and increase of fuel concentration there is suppressed. The dilution air is preferably supplied from gas turbine compressor (6). <IMAGE></p>