A gas turbine combustor, in which plural pre-mixers that inject fuel into swirling air passages are arranged to surround a pilot burner, and a pilot flame, guided by a pilot cone in the shape of a flaring pipe and provided at the rear end of the pilot burner, is mixed with a pre-mixture blown out from the pre-mixers to obtain a combustion gas, comprising flame-stabilizing means. The flame-stabilizing means lower the disturbance in a region where the pre-mixture and the pilot flame are mixed or stabilize the pilot flame, so that the flame generated by igniting the pre-mixture with the pilot flame is stabilized. By stabilizing the flame, combustion with a leaner air-fuel ratio is possible, and thereby the amount of NOx can be decreased.