Cable-Driven Parallel Robots (CDPRs) have been proposed for a variety of applications such as material handling, rehabilitation, and instrumentation. However, the collision-free constraint of CDPRs limits the workspace of CDPRs and the feasible position of anchor points. To address the collision-free constraint of CDPRs, a data-driven kinematic control scheme is developed for CDPRs, enabling a CDPR to control its pose even if suffering collisions between a cable and the base or the end-effector. To deal with the collisions, the data-driven kinematic control scheme utilizes a motion model obtained based on data samples of the motion of the CDPR, rather than the Jacobian matrix of the CDPR, to map a control law in the task space to the time derivative of the length of cables in the joint space. To evaluate the effectiveness of the developed data-driven kinematic control scheme, experiments of controlling a suspended CDPR with two cables allowing collisions are conducted.