Adhesion of particulate matters to the burner accompanying combustion in a lean-combustion gas turbine combustor is suppressed, and the structural reliability is improved. In a gas turbine combustor including: a tubular liner that forms a combustion chamber; and a burner including an air hole plate that is arranged at an inlet of the liner and includes a plurality of air holes for guiding compressed air to the combustion chamber, and a plurality of fuel nozzles that are arranged on a side opposite to the combustion chamber with the air hole plate being sandwiched therebetween, the plurality of fuel nozzles each injecting a fuel toward a corresponding air hole, the air holes and the fuel nozzles forming a plurality of concentric annular lines, a plurality of small holes having opening diameters smaller than those of the air holes are provided through the air hole plate such that the plurality of small holes are positioned in an inner area of an innermost annular line of the air holes.