Aiming at the problem of compliance control and response speed in robot polishing of curved surface components, a set of compliance control system for robot polishing was studied. The slicing algorithm was used to complete the polishing trajectory planning to control the robot to comply with the low-frequency profile and curvature changes of the surface of curved components. A force controlled end effector was designed to meet the requirements of active force output and high-speed response. The current iterative optimization control strategy based on iterative learning control was proposed to make the output force of voice coil motor in the actuator follow the target force with high accuracy, reducing the waviness and surface roughness of the high-frequency segment of the surface of components. An experimental platform with robots, force control actuators, six dimensional force sensors and motion control cards as the core components was built. The simulation and experimental results show that the designed compliance control system has good force control performance, the average force response time is 55.4 ms, and the force tracking error is less than 3 N, which can meet the needs of surface component polishing.