A gas turbine combustor having an improved cooling structure effective to efficiently suppress a possible occurrence of buckling in the combustion liner while exhibiting a convection cooling effect to the combustion liner, the gas turbine combustor includes a combustion liner having a combustion chamber defined therein and an outer peripheral surface forming a path of a compressed air, and a heat transfer enhancement structure provided on the outer peripheral surface of the combustion liner. The heat transfer enhancement structure referred to above is of a honeycomb construction defined by ribs protruding outwardly from the outer surface of the combustion liner. The honeycomb construction may be of a geometry in which hexagonal shapes, rhombic shapes, parallelogrammic shapes, bent rectangular shapes or triangular shapes are deployed next to each other.