Gas turbine engines are used in various fields. In the field of land, they are mainly used for power generation. The use in the aviation field is for aircraft and fighter jets. In the marine field, they have been used in warships, offshore plants and some merchant ships. The performance of gas turbine engines operated in the marine field varies depending on the characteristics of the place where they are used and the marine environment. And the engine parameter values change when the operating point changes. This thesis presents the F-PID(Fuzzy-PID) controller for accurate and rapid speed control of the gas turbine engine with these characteristics. The model is the LM-2500 and it is the gas turbine engine widely used in the marine field. Based on the sea trial data, the parameters of the gas turbine engine model at a specific operating point are obtained. For the gas turbine engine modeling, a commonly used FOPTD model is selected for a gas generator, and the FMU(fuel metering unit) is represented by a second-order linear model. In this thesis, the cascade system is considered as a control target by combining the gas generator and the FMU. A sub-model of the gas turbine engine is obtained at three operating points, and a T-S fuzzy model is derived to reflect the non-linearity of the gas turbine engine. The controller is designed so that the rotor speed tracking control can be stably applied to the fuzzy model reflecting the parameter variability of the gas turbine engine according to the change of the operating point. Sub-controllers are optimized R-PID controllers using RCGA. The superiority of the R-PID controller is verified by comparing the R-PID controller and the PID controller of other tuning methods. The F-PID controller is performed with the combination of these sub-controllers by fuzzy IF-THEN rules. The efficacy of the proposed F-PID controller is verified by performing simulations, which apply the R-PID controllers and the F-PID controller to the T-S fuzzy model.