In the past decades, cable-driven parallel robots (CDPRs) have been proven the extraordinary performance for various applications. However, the multiple cables lead the robot easy to interfere with environments. Especially the large workspace of CDPR may introduce unknown moving obstacles. In this study, a sampling-based path planning method is presented for a CDPR to find the collision-free path in the presence of the moving obstacle. The suggested method is based on rapidly exploring random tree (RRT) algorithm which gives CDPRs advantages to handle complex constraints such as cable collision and dynamic feasible workspace (DFW). Moreover, we conduct the forward simulation to check the feasibility in a closed-loop system. The moving parts of both CDPRs and the moving obstacle are assumed as convex bodies, so that Gilbert-Johnson-Keerthi (GJK) algorithm is adopted to detect collision in real-time. Finally, the related simulation is carried out to illustrate the algorithm. The experiment is also presented using the drone as a moving obstacle and YOLO vision algorithm to detect the drone. The experiment results demonstrate the reliability of the suggested method.