This paper investigates a closed-loop visual servo control scheme for controlling the position of a fully constrained cable-driven parallel robot (CDPR) designed for functional rehabilitation tasks. The control system incorporates real-time position correction using an Intel RealSense camera. Our CDPR features four cables exiting from pulleys, driven by AC servomotors, to move the moving platform (MP). The focus of this work is the development of a control scheme for a closed-loop visual servoing system utilizing depth/RGB images. The developed algorithm uses this data to determine the actual Cartesian position of the MP, which is then compared to the desired position to calculate the required Cartesian displacement. This displacement is fed into the inverse kinematic model to generate the servomotor commands. Three types of trajectories (circular, square, and triangular) are used to test the controller’s compliance with its position. Compared to the open-loop control of the robot, the new control system increases positional accuracy and effectively handles cable behavior, various perturbations, and modeling errors. The obtained results showed significant improvements in control performance, notably reduced root mean square error and maximal error in terms of position.