A gas turbine combustor comprising a head combustion chamber and a rear combustion chamber connected to a downstream side of the head combustion chamber, a first stage burner for premixing first stage fuel and air and supplying the resultant fuel and air premixture into the head combustion chamber to effect first stage premix combution, a second stage burner for premixing second stage fuel and air and the resultant fuel and air premixture into the rear combustion chamber to effect premix combustion in addition to the first stage premix combustion, and a device for regulating flow rates of combustion air to be premixed with first and second stage fuel. The combustor is further provided with a pilot burner in the head combustion chamber to form pilot flame and stabilize the first stage premix combustion.