In a burner for injecting mixed gas fuel containing at least one of hydrogen and carbon monoxide into a combustion chamber of a gas turbine combustor, the burner includes a fuel nozzle for startup from which liquid fuel is injected into the combustion chamber, and a mixed fuel nozzle disposed around the fuel nozzle for injecting the mixed gas fuel. An air swirler is disposed at a downstream end of the mixed fuel nozzle and has a plurality of flow passages from which compressed air is injected into the combustion chamber, and the mixed fuel nozzle has injection ports disposed in the inner peripheral side of the flow passages of the air swirler. Cooling holes formed in the nozzle surface and positioned to face the combustion chamber introduce a part of the mixed gas fuel injected from the mixed fuel nozzle into the combustion chamber.