Computer Control Optics Surfacing (CCOS) requires the surface error map for iterative processing to get low error by dwellingtime caculation. Because the smaller aperture of error map will be gotten in interferometer on edge of optic work part, so the predictive extrapolation of surface error map is the basic technology of magneto-rheological polishing, ion beam polishing and other machining methods. Based on the similarity of surface error and the continuity of edge error, the extrapolation of surface error method was developed, based on Zernike fitting and Laplace equation. The theory was studied and the algorithm was developed to get extrapolation of surface error map, fulfilling the similarity and the continuity. The result was evaluated by surface error comparison and residual error calculation, which was proved to be effective.