In this paper, a high precision polishing robot with a learning-based surface following controller is proposed for polishing PET (poly ethylene terephthalate) bottle molds with curve surface. The shape of a mounted abrasive tool, attached to the tip of the robot arm, is a ball-end type. When a PET bottle mold with a large curvature is polished, not only the orientation of the mounted abrasive tool is fixed but also its revolution is locked. The motion of the mounted abrasive tool is feedforwardly controlled based on initial trajectory calculated in advance. The trajectory is generated by cutter location data constituted from a CAM system. The trajectory is modified through the process of actual polishing. The surface is polished by a polishing force acting between the mold and the abrasive tool. The polishing force is assumed to be considered as a composite force of the contact and kinematic friction forces, in which the friction consists of Coulomb and viscous frictions. Velocities in the normal and tangent directions are delicately controlled so that the proposed system is effective for obtaining a polishing surface as achieved by skilled workers.