A Model Predictive Control (MPC) strategy is proposed in this paper for large-dimension cable-driven parallel robots working at low speeds. The latter characteristic reduces the non-linearity of the system within the MPC prediction horizon. Therefore, linear MPC is applied and compared with two commonly used strategies: Sliding mode control and PID+ control. The simulations aim at comparing disturbance rejection performances and the results indicate a superior performance of the proposed controller. Indeed, MPC takes into account control limits (cable tension limits) directly in the control design which allows the controller to better exploit the robot capabilities. In addition, actuation redundancy is resolved as an integral part of the control strategy, instead of calculating the desired wrench and then applying a tension distribution method.