In a structure for cooling a component member of a gas turbine using a working gas, a plurality of heat transfer enhancement ribs having W shapes are provided so as to project from the wall surface of a passage wall facing a cooling medium passage through which a cooling medium flows. In each heat transfer enhancement rib, outside corner portions facing toward the upstream side are formed in an angled shape, and at least any one of inside corner portions and outside corner portions other than the outside corner portion facing toward the upstream side are formed in a curved shape.