This article introduces the design and control performance of a lightweight, flexible, 4-degree-of-freedom (DOF) parallel robot for percutaneous biopsy guided by computed tomography (CT). At present, the CT guidance method allows surgeons to quickly locate the lesion area; however, it is necessary to manually adjust the position of the puncture needle for insertion. In this paper, a three-dimensional assisted method is used to infer the control input required to reach the target point through the kinematic model of the robot. A Kalman filter is designed to estimate model parameters and obtain a more accurate model. To further improve the control performance of the robot system, a model-based control method—the model predictive control (MPC) controller—is used to increase the accuracy of the needle position in the developed robot system. In this way, medical efficiency is improved while reducing the burden on the surgeon.