To prevent or reduce an oversensitive change in the degree of opening of a bleed valve regulating the flow volume of a cooling air used to heat a fuel. A gas turbine includes: a compressor compressing an air; a combustor burning a fuel mixed with the air compressed by the compressor; a turbine configured to be driven by a combustion gas generated by the combustor; a heat exchanger causing the fuel to be supplied to the combustor to be heated through a cooling air bled from the compressor to be supplied to the turbine; a bleed valve regulating the flow volume of the cooling air; a first sensor measuring a fuel state value; a second sensor measuring a cooling air state value; and a control computer controlling the degree of opening of the bleed valve. The control computer stores therein data on reference values and dead bands including the corresponding reference value set for each of the fuel state value and the cooling air state value, and, when a measured value of at least one of the fuel state value and the cooling air state value has changed so much away from the corresponding reference value as to fall outside the corresponding dead band, controls the bleed valve such that the changed measured value is brought close to the corresponding reference value.