In cooling a gas turbine stationary blade, steam and air are used as cooling media, the steam is recovered surely without leakage and used effectively, and the amount of air required for cooling is decreased to provide a margin for combustion air, by which the gas turbine efficiency is improved. A steam cooling section is provided at the rear from the blade leading edge, and an air cooling section is provided at the blade trailing edge. The steam cooling is effected by cooling the blade by the cooling steam flowing in the serpentine flow path having turbulators after impingement cooling of an outside shroud and by impingement-cooling an inside shroud during the cooling process, the cooling steam being led to a recovery section from the outside shroud. On the other hand, the air cooling section consists of an air flow path extending from the outside shroud to the inside shroud and slot cooling at the blade trailing edge. Thus, the stationary blade is cooled by both of the steam cooling section and air cooling section.