In a structure for internally cooling a turbine blade, a cooling medium passage is provided in the turbine blade. The cooling medium passage has a shape in which a plurality of cylindrical spaces, each having substantially cylindrical shape, extending in parallel with each other partially overlap each other. A cooling medium supply passage that supplies a cooling medium to the cooling medium passage is connected to a portion of the cooling medium passage that includes a peripheral wall, in a direction that forms an acute angle with respect to a longitudinal direction of the cooling medium passage.