In a gas turbine combustor 3 of the present invention, an air hole plate 20 includes a center air hole group 51 configured from a plurality of air holes 51A and 51B and a plurality of outer circumferential air hole groups 52 configured from a plurality of air holes 52A, 52B, and 52C and formed to surround the center air hole group 51. The gas turbine combustor 3 includes a hole part 601 and a temperature sensor 401 provided on the air hole plate 20 to be located in a region surrounded by two outer circumferential air hole groups 52 adjacent to each other and the center air hole group 51, a supply source 220 of coolant, a cooling pipeline 205 that connects the hole part 601 and the supply source 220, valves 67 and 68 provided in the cooling pipeline 205, and a control system 500 that drives the valves 67 and 68 on the basis of a measured value of the temperature sensor 401.