Cable-Driven Parallel Robots (CDPRs) can execute fast motions across a large workspace. However, these performances are reached at the cost of a relatively low stiffness which often yields parasitic vibrations at the CDPR mobile platform. In this paper, vibration damping of CDPRs is addressed by means of an original active stabilizer consisting of actuated rotating arms installed on-board the CDPR mobile platform. A control strategy for the whole system, which consists of the CDPR and the stabilizer, and with one purpose for each-position control for the platform and vibration damping for the stabilizer-is designed. The system being controlled at two different time scales, the singular perturbation theory can be used to prove the stability of the corresponding closed-loop system. The efficiency of the proposed device and control strategy is tested in simulations in the case of a planar 3-DOF CDPR equipped with a three-arm stabilizer.