Magnetic resonance imaging (MRI)-guided robot for puncture surgery has developed rapidly in recent years. However, the robot’s design is challenged by the limited workspace and strong magnetic field inside the MRI scanner. For prostate puncture surgery, this paper proposes an MRI-compatible cable-driven robot for puncture surgery. The wrench feasible workspace of the robot under three different cable layout structures is analyzed, and the optimal configuration is selected to design the robot. The cable layout size of the robot is reduced to a circle with a diameter of 150 mm, which can meet the workspace requirements inside the scanner. Different puncture trajectories are planned in the simulation, which proves the feasibility of the cable-driven puncture surgical robot. In the real-time experiment, the average response time of the robot control system is 0.024 s. In the translational motion experiment, the cable length error is ±0.28mm, and in the process of repeated insertion, the cable length error is ±0.5mm. The average position error of the puncture needle in the process of puncture at different angles is 0.31 mm, and the average position error when subjected to external shocks is 0.32 mm. The robot proposed in this study has potential application value in special environments. It proposes a new solution for the design of puncture surgical robots used in strong magnetic fields.