To accurately describe the dynamic response process of helicopter maneuvering flight, this study combines the engine aero-thermodynamic model with the helicopter flight dynamics model to establish a coupled model of helicopter/engine that reveals the effect of rotor speed variation. Firstly, the rotor flight dynamics model and the engine’s component-level aero-thermodynamic models are established. Then, the rotor/engine coupling model is formulated based on the power matching relationship, ultimately forming a coupled model of helicopter/engine that accounts for the engine’s dynamic characteristics. The UH-60A flight test data are used to validate the trim and dynamic response of the helicopter model. The results show that the helicopter model can accurately describe rotor speed and yaw moment changes. Finally, a simulation was performed on the helicopter bob-up maneuver flight process. The study shows that the helicopter flight state changes rapidly during the bob-up maneuver, and the rapid change in engine load causes a sudden change in rotor speed, leading to a reverse change in yaw angular velocity in the yaw direction, which has adverse effects on the helicopter’s maneuverability. This research has important reference value for a deeper understanding of the coupling relationship between helicopter and engine, improving the design of helicopter/engine coupling control laws, and enhancing helicopter maneuver flight performance.