A method for operating a gas turbine combustor including: a casing; a combustor liner which is disposed in the casing and combusts a fuel and an oxidant; a fuel supply part which supplies the fuel to the combustor liner; an oxidant supply part which supplies the oxidant to the combustor liner; and a controller which controls a flow rate of the fuel supplied from the fuel supply part and a flow rate of the oxidant supplied from the oxidant supply part, wherein, in the gas turbine combustor, an exhaust gas discharged from a turbine is circulated in the casing through a circulation system connecting an outlet of the turbine and the casing as a circulating gas, and the circulating gas is introduced into the combustor liner through through holes (22, 23) provided in the combustor liner, the method being characterized by comprising: circulating, before ignition in the gas turbine combustor, a mixed gas containing oxygen in a predetermined concentration as the circulating gas; and circulating, in an operating time from a time of ignition in the gas turbine combustor to a time of a rated load of the turbine, from the time of ignition until reaching stable combustion conditions allowing stable combustion, a combustion gas as the circulating gas, the combustion gas being maintained at a same oxygen concentration as an oxygen concentration in the mixed gas by controlling the flow rate of the fuel supplied from the fuel supply part and the flow rate of the oxidant supplied from the oxidant supply part by the controller. a casing; a combustor liner which is disposed in the casing and combusts a fuel and an oxidant; a fuel supply part which supplies the fuel to the combustor liner; an oxidant supply part which supplies the oxidant to the combustor liner; and a controller which controls a flow rate of the fuel supplied from the fuel supply part and a flow rate of the oxidant supplied from the oxidant supply part, wherein, in the gas turbine combustor, an exhaust gas discharged from a turbine is circulated in the casing through a circulation system connecting an outlet of the turbine and the casing as a circulating gas, and the circulating gas is introduced into the combustor liner through through holes (22, 23) provided in the combustor liner, the method being characterized by comprising: circulating, before ignition in the gas turbine combustor, a mixed gas containing oxygen in a predetermined concentration as the circulating gas; and circulating, in an operating time from a time of ignition in the gas turbine combustor to a time of a rated load of the turbine, from the time of ignition until reaching stable combustion conditions allowing stable combustion, a combustion gas as the circulating gas, the combustion gas being maintained at a same oxygen concentration as an oxygen concentration in the mixed gas by controlling the flow rate of the fuel supplied from the fuel supply part and the flow rate of the oxidant supplied from the oxidant supply part by the controller. circulating, before ignition in the gas turbine combustor, a mixed gas containing oxygen in a predetermined concentration as the circulating gas; and circulating, in an operating time from a time of ignition in the gas turbine combustor to a time of a rated load of the turbine, from the time of ignition until reaching stable combustion conditions allowing stable combustion, a combustion gas as the circulating gas, the combustion gas being maintained at a same oxygen concentration as an oxygen concentration in the mixed gas by controlling the flow rate of the fuel supplied from the fuel supply part and the flow rate of the oxidant supplied from the oxidant supply part by the controller.