A gas turbine combustor including a fuel injector having a plurality of annular fuel injection portions in each of which multiple fuel injection holes are formed, is provided with: an auxiliary fuel introduction passage for introducing an auxiliary fuel that is to be supplied to an auxiliary fuel injection portion that is a part of the plurality of annular fuel injection portions, into the fuel injector; a first main fuel introduction passage provided with a flow regulating valve for introducing a main fuel that is to be supplied to a main fuel injection portion that is an annular fuel injection portion other than the auxiliary fuel injection portion, into the fuel injector; and a second main fuel introduction passage provided with a flow regulating valve for introducing the main fuel that is to be supplied to the auxiliary fuel injection portion, into the fuel injector.