Gas turbine engines are often used in propulsion systems and power supply systems to meet the Required Operational Capability of Warships. A precise speed control system is necessary for the stable performance of such a gas turbine engine. Detailed mathematical modeling and sophisticated controller design are critical to achieving excellent control response in a variety of warship operating environments. In this paper, an IMC-based PID controller design method is proposed that can simultaneously improve set-point tracking and disturbance suppression performance of warship propulsion gas turbine engines. The engine is modeled by dividing it into a gas turbine assembly and a fuel metering unit. First, the gas turbine assembly is represented as a first-order linear model at four operating points, and then uses warship commissioning data to secure the realism and accuracy of the mathematical model. Next, the fuel metering unit is represented as a Second-order linear model and combined with the gas turbine assembly model to derive the entire control object. For model-based controller design, the control object is approximated to a FOPTD model. This approximated FOPTD model is derived in the form of a PID controller using the IMC technique, and an IMC-based PID controller with excellent tracking performance and disturbance suppression ability is designed. The designed controller comprehensively performs simulation by applying it to the nominal model and the parameter uncertainty model in the four operating areas, and verifies the validity and robustness of the proposed controller compared with the existing control method.