Abstract: In the ion beam figuring technique, to improve the solution precision of the dwell time algorithm on the edge of the component, the initial surface of the error should be extended smoothly and limited. A curve surface extending algorithm was proposed which is based on the Gaussian curve. The character of smooth, limitary and parameter continuity were used. When the curve surface extending method was used in the dwell time solving process of a surface error with high frequency noise, the residual error of the dwell time algorithm on the edge was controlled. The ratio of the surface error constringency in the whole caliber reached 97% by RMS. The results show that the surface extending algorithm which based on the Gaussian curve can extend the surface error of optics smoothly. And it has good ability to oppose the noise disturbance. It improved the solution precision of the dwell time algorithm.