To improve the response rate and control accuracy of the permanent magnet synchronous motor servo system, this paper proposes a generalized predictive control approach with enhanced disturbance rejection ability in continuous time domain. Firstly, the model parameter perturbations and external uncertain load disturbances are estimated by constructing a high-order extended state observer, and thereby the estimated information of disturbance and rotor angular velocity is introduced into the position trajectory output prediction sequence to realize the correction of the prediction model errors. Furthermore, by solving the optimization problem of the position tracking error performance index, the explicit analytical solution of the optimal control sequence is obtained, and the selection guideline of control gains is theoretically given. Finally, the Lyapunov theory is employed to conduct a rigorous stability analysis of the closed-loop system, and the controller performance is verified by using a rapid control prototype drag loading experimental platform. The experimental results show that, compared with the cascade PI control method and the traditional generalized predictive control method, the proposed control method improves the position tracking accuracy and the disturbance rejection ability of the servo system.