This paper addresses the force-tracking problem of aerospace electro-hydraulic load simulators under the influence of high inertia, large loads, and a strong coupling force disturbance. An accurate mathematical model is initially derived to describe the characteristics of the load simulator system, the cause of the surplus force, and the strong phase lag due to large inertia. In order to overcome the position interference of the system and the large phase lag problem, a terminal sliding mode control strategy based on the modified fast double-power reaching law is proposed, based on the accurate mathematical model. This control strategy effectively suppresses the chattering problem of the sliding control and implements the finite time convergence of the system through the design of the reaching law and terminal sliding surface, ensuring the robustness of the system and the accuracy of the force-tracking problem. Finally, a comparison of the simulation and experimental results based on the design of different strategy controllers is performed to verify the effectiveness of the control strategy and system adaptability.