In this article, a predictor-based model reference adaptive control method is proposed for a JetCat SPT5 turboshaft engine in full thrust, cruise, and idle modes. In the predictor-based model reference adaptive control method, in addition to the tracking error, the predictor error is also utilized in adaptive laws to achieve the desired control objectives, such as improving the tracking performance and control signals, and reducing the tracking error. The proposed method is implemented on a turboshaft engine system with actual dynamic values. First, three properly separated equilibrium points are selected on the nominal plant equilibrium manifold to linearize the plant model at the equilibrium points. Then, the predictor-based model reference adaptive control controller is designed and investigated for the three equilibrium points generating three operating modes of the engine, that is, full thrust, cruise, and idle. The stability of the control system is proved by the Lyapunov method. To evaluate the efficiency of the state predictor method in the simulation scenarios, the proposed method is compared with the classic model reference adaptive control method. The simulation results illustrate the superiority of the predictor-based model reference method due to the reduction of unwanted fluctuations in tracking performance, faster convergence of the tracking error to zero, and smoother control signals for all the equilibrium points.