Precision polishing system for opticals based on bonnet polishing technology and industrial robot can not only meet the requirements of high efficiency and precision of rapid polishing, but also reduce the development cost, thus it is a potential development solution for polishing. Bonnet polishing requires stable and deterministic material removal characteristics, and the stability of polishing spot is usually around 90%. The influence of robot stiffness on the stability of robot bonnet polishing system in the process of multi-step discrete precession polishing was studied. The robot end deformation was analyzed by the stiffness matrix, and the removal function of bonnet polishing with deformation error was established based on Preston theory. Finally, a four-step discrete polishing experiment was designed. According to the results, the polishing spot was Gaussian on the xy section contour line, and the xy section contour line was basically the same, with a good coincidence degree. Comparison of the cross-section profiles at different polishing positions indicates, the relative errors are below 5%. The experiment proves that the robot bonnet polishing system has a good stability in discrete precast polishing.