A gas turbine can efficiently be cooled by using steam, without using high-pressure steam generated in an exhaust-heat recovery boiler and without decreasing the high-pressure steam generation. This cooling system is provided with a gas turbine; an exhaust-heat recovery boiler having a high-pressure system that generates high-pressure steam by means of heat exchange with exhaust heat from the gas turbine, a high-pressure drum that supplies water and steam to the high-pressure system, a medium-pressure system that generates medium-pressure steam by means of heat exchange with the exhaust heat from the gas turbine, and a medium-pressure drum that supplies water and steam to the medium-pressure system; a medium-pressure steam pipe that connects the medium-pressure system and a cooling system of the gas turbine and that supplies the medium-pressure steam from the medium-pressure system to the cooling system; and a steam supplying pipe that connects the high-pressure drum and the medium-pressure drum.