The hyper-redundant manipulators are suitable for working in the constrained on-orbit servicing environment due to the extreme flexibility. However, its modelling and control are very challenging due to the characteristics of non-linearity and strong coupling. In this paper, considering the multi-level mapping among the motors, cables, joints, and end-effector, a proportional derivative (PD) with dynamic feedforward compensation control system is designed. The corresponding control system is divided into five parts: controller, planner, actuator, manipulator, and sensor. The actual control torque consisting of the desired feedforward torque and the feedback torque is generated by the controller. In order to improve the tracking accuracy and maintain rapid response, the torque, which is calculated by the dynamics model of the traditional joint-driven manipulator, is regarded as the desired feedforward torque. The parameters of interest are the angle and velocity of the universal joint and motors. The planner plans and converts the desired parameters of the universal joint to corresponding motors. Combining with the feedback angles and velocities signals of the corresponding motors, the feedback torque can be calculated by the PD control module. Finally, typical cases of six universal joints (12DOFs) manipulators are simulated and experimented. The results demonstrate that the method is very efficient for controlling spatial cable-driven hyper-redundant manipulators.