A gas turbine combustor includes plural multi-coaxial-injection-hole burners in which plural fuel nozzles and plural air holes provided in an air plate to correspond to the respective fuel nozzles are coaxially arranged. Each of the multi-coaxial-injection-hole burners includes a first coaxial injection burner disposed on an inner circumferential side, and a second coaxial injection burner disposed on an outer circumferential side, and a diameter of the air holes of the first coaxial injection burner is smaller than a diameter of the air holes of the second coaxial injection burner. Combustion for carrying out flame holding of a gas turbine combustor is performed by the first coaxial injection burner, and low NOx combustion of the gas turbine combustor is performed by the second coaxial injection burner.