A structure for cooling a turbine airfoil includes: a cooling passage formed between a first airfoil wall curved as to be concave relative to a high-temperature gas passage and a second airfoil wall curved so as to be convex relative to the high-temperature gas passage; lattice structure bodies each formed by stacking a plurality of ribs in a lattice pattern; a partition body provided between the adjacent lattice structure bodies; a cooling medium discharge port for discharging a cooling medium within the cooling passage to the outside; and an exposed wall portion formed as a portion of the second airfoil wall extending beyond the cooling medium discharge port to the outside. At outlet portions of the lattice structure bodies adjacent to each other across the partition body, adjacent first rib sets and second rib sets are inclined in opposite directions relative to the partition body, respectively.