A gas turbine cooling system includes: a cooling air line that guides compressed air; a cooler that cools the compressed air; a flow rate adjuster that adjusts the flow rate of the cooling air; and a control device. The control device includes: a load change determination unit that determines whether a load indicated by a load command of the gas turbine has changed; a first command generation section that generates a first command indicating such an operation amount of the flow rate adjuster as allows the flow rate of the cooling air to meet a target flow rate; and a second command generation section that, when it is determined that the load indicated by the load command has changed, generates a second command indicating such an operation amount of the flow rate adjuster as allows a change-adapted flow rate higher than the target flow rate to be met.