To study the trajectory tracking and vibration suppression of a multi-variable high-dimensional spatial rigid-flexible coupling closed-chain robot, a PD control method based on feedforward compensation was proposed. The flexible spatial links were discreted by finite element method, and then the displacement field vector of the flexible links was described based on the floating frame of reference formulation, and the dynamic model of the rigid-flexible coupling spatial parallel robot was established considering the small displacement of the rigid end effector according to the Lagrange equation. The feedforward control was used to compensate the control torque with the coupling effects obtained in advance, which improved the response speed and tracking performance of the rigid-flexible coupling control system. At the same time, the PD control law was used to ensure the trajectory accuracy of the spatial closed-chain robot, and the trajectory tracking accuracy under different end loads was analyzed, and finally it was compared with the position PID algorithm. The results showed that the trajectory accuracy of the rigid end effector under the control algorithm was effectively improved relative to the trajectory accuracy under the position PID algorithm. Among them, the error in the X direction was reduced by 89.7%, the error in the Y direction was reduced by 4.3%, and the error in the Z direction was reduced by 12.9%, the vibration generated by the flexible spatial links was suppressed, and the effectiveness of the controller design was verified.