A gas turbine combustor into which steam with a variable flow rate is injected and which burns fuel with compressed air from a compressor to generate combustion gas, the gas turbine combustor comprising: a tubular combustion liner that defines therein a combustion chamber, the combustion liner having a plurality of dilution holes disposed at circumferentially spaced intervals at a section downstream in a direction of flow of the combustion gas; and a combustor casing that encloses the combustion liner, wherein the gas turbine combustor further comprises: a liner flow sleeve disposed between the combustion liner and the combustor casing, to define with the combustion liner an annular air flow path through which the compressed air flows, characterized in that, said liner flow sleeve has a plurality of steam injection holes; and a steam distribution mechanism (31, 33; 55) disposed on an outer peripheral side of the liner flow sleeve, the steam distribution mechanism receiving the injected steam and distributing the received steam to the steam injection holes, wherein at least some of the steam injection holes are disposed so as to face at least some of the dilution holes, and the steam injection holes facing the respective dilution holes are each formed so as to spurt the steam toward the corresponding dilution hole that faces the steam injection hole, and wherein the steam distribution mechanism includes: a steam injection port into which the steam is injected, the steam injection port being disposed at the combustor casing; and a steam header having on an inner peripheral side of the combustor casing an annular space that receives the steam from the steam injection port, the steam header distributing the steam from the steam injection port to the steam injection holes. a tubular combustion liner that defines therein a combustion chamber, the combustion liner having a plurality of dilution holes disposed at circumferentially spaced intervals at a section downstream in a direction of flow of the combustion gas; and a combustor casing that encloses the combustion liner, wherein the gas turbine combustor further comprises: a liner flow sleeve disposed between the combustion liner and the combustor casing, to define with the combustion liner an annular air flow path through which the compressed air flows, characterized in that, said liner flow sleeve has a plurality of steam injection holes; and a steam distribution mechanism (31, 33; 55) disposed on an outer peripheral side of the liner flow sleeve, the steam distribution mechanism receiving the injected steam and distributing the received steam to the steam injection holes, wherein at least some of the steam injection holes are disposed so as to face at least some of the dilution holes, and the steam injection holes facing the respective dilution holes are each formed so as to spurt the steam toward the corresponding dilution hole that faces the steam injection hole, at least some of the steam injection holes are disposed so as to face at least some of the dilution holes, and the steam injection holes facing the respective dilution holes are each formed so as to spurt the steam toward the corresponding dilution hole that faces the steam injection hole, a steam injection port into which the steam is injected, the steam injection port being disposed at the combustor casing; and a steam header having on an inner peripheral side of the combustor casing an annular space that receives the steam from the steam injection port, the steam header distributing the steam from the steam injection port to the steam injection holes.