A gas turbine combustor having a head combustion chamber and a rear combustion chamber, with a plurality of air supply ports arranged in a circumferential wall of the rear combustion chamber, and a fuel nozzle. An outer cylinder forms a cylindrical air flow passage between the inner cylinder and the outer cylinder. A cylindrical control member is provided which is adapted to be movable in an axial direction for regulating an opening of the air supply ports. The control member is supported by a supporting means which is adapted to maintain a gap between the control member and the wall of the rear combustion chamber. The supporting member includes a flexible member for absorbing a deformation of the control member during the axial movement of the control member so that it is possible to prevent, if not avoid, mechanical wear on the control member and to reduce the No.sub.x concentration as well as obtain a highly reliable operation of the gas turbine combustor.