Precise control is of importance for robots, whereas, due to the presence of modeling errors and uncertainties under the complex working environment, it is difficult to obtain an accurate dynamic model of the robot, leading to decreased control performances. This work presents an open-closed-loop iterative learning control applied to a four-limb parallel Schönflies-motion robot, aiming to improve the tracking accuracy with high movement, in which the controller can learn from the iterative errors to make the robot end-effector approximate to the expected trajectory. The control algorithm is compared with classical D-ILC, which is illustrated along with an industrial trajectory of pick-and-place operation. External repetitive and non-repetitive disturbances are added to verify the robustness of the proposed approach. To verify the overall performance of the proposed control law, multiple trajectories within the workspace, different working frequencies for a prescribed trajectory, and different design methods are selected, which show the effectiveness and the generalization ability of the designed controller