The invention aims to shorten the time required for start-up and prevent excessive increases in the heat loads on turbine blades. A humid air turbine includes a compressor; a combustor; a turbine; an exhaust heat recovery unit for recovering the heat of turbine exhaust gas to generate high-temperature moisture; a fuel supply system having a fuel flow rate control valve; an exhaust temperature acquiring unit for acquiring a temperature of the exhaust discharged while the turbine is driven; a combustion gas moisture ratio calculating section for calculating a ratio of moisture contained in combustion gas; an exhaust temperature upper limit calculating section for setting an exhaust temperature upper limit based on the combustion gas moisture ratio and the pressure ratio; an exhaust temperature difference calculating section for calculating the difference between the exhaust temperature upper limit and the exhaust temperature; a fuel flow rate command value calculating section for calculating a fuel flow rate command value using the exhaust temperature difference; and a control command value output section for outputting a command signal to the fuel flow rate control valve based on the command value selected by a fuel flow rate command value selecting section.