A gas turbine combustor comprising: at least one premixing burner (76, 77) for premixing gaseous fuel with air and jetting the mixed gas into a chamber; a cylindrical guide disposed on an outer circumference of the premixing burner (76, 77) so as to surround the premixing burner (76, 77) and connected to a burner outlet end face which is an end face of the premixing burner (76, 77) on the chamber side; and a plurality of air supply holes formed in the cylindrical guide; wherein an interval defined between the adjacent air supply holes is 1cm or less so as to be smaller than a quenching distance in the premixed gas jetted from the premixing burner (76, 77), and wherein an interval defined between each air supply hole and the burner outlet end face is 1cm or less so as to be smaller than the quenching distance in the premixed gas jetted from the premixing burner (76, 77), wherein the gas turbine combustor further comprises: a liner for surrounding the chamber; and a seal member disposed between the liner and the cylindrical guide inserted into the liner to secure the cylindrical guide and the liner, the seal member obstructing a flow of air between the liner and the cylindrical guide; wherein the air supply holes formed in the cylindrical guide are disposed in a range from an upstream end of the seal member to a downstream end thereof with respect to a flow direction of the air flowing down through a gap between the liner and the cylindrical guide. at least one premixing burner (76, 77) for premixing gaseous fuel with air and jetting the mixed gas into a chamber; a cylindrical guide disposed on an outer circumference of the premixing burner (76, 77) so as to surround the premixing burner (76, 77) and connected to a burner outlet end face which is an end face of the premixing burner (76, 77) on the chamber side; and a plurality of air supply holes formed in the cylindrical guide; wherein an interval defined between the adjacent air supply holes is 1cm or less so as to be smaller than a quenching distance in the premixed gas jetted from the premixing burner (76, 77), and wherein an interval defined between each air supply hole and the burner outlet end face is 1cm or less so as to be smaller than the quenching distance in the premixed gas jetted from the premixing burner (76, 77), wherein the gas turbine combustor further comprises: a liner for surrounding the chamber; and a seal member disposed between the liner and the cylindrical guide inserted into the liner to secure the cylindrical guide and the liner, the seal member obstructing a flow of air between the liner and the cylindrical guide; wherein the air supply holes formed in the cylindrical guide are disposed in a range from an upstream end of the seal member to a downstream end thereof with respect to a flow direction of the air flowing down through a gap between the liner and the cylindrical guide. a liner for surrounding the chamber; and a seal member disposed between the liner and the cylindrical guide inserted into the liner to secure the cylindrical guide and the liner, the seal member obstructing a flow of air between the liner and the cylindrical guide; wherein the air supply holes formed in the cylindrical guide are disposed in a range from an upstream end of the seal member to a downstream end thereof with respect to a flow direction of the air flowing down through a gap between the liner and the cylindrical guide.