As the consumer market in the optics, electronics and aerospace industries grows, the profile accuracy demand for ultra-precision flat, spherical and aspheric optical surface micro-lens increases. Previous studies have found that machine system accuracy, tool alignment error and tool radius measurement error impact greatly on the profile accuracy of the machined surface. In this paper, we developed a grinding system based on the ultra-precision diamond lathe, presented a unified mathematical model of effects of all the geometric errors to the shape error by using the multi-body system theory. Aiming at the main source of profile error, the practical mathematical model is derived, and their propagation coefficients to profile error are calculated. By means of simulation analysis and grinding experiments of spherical part of tugnsten carbide, we conclude that the radial tool alignment error is the main influencing factor for the profile error of spherical surface; while tool radius measurement error influence the radius of sphere only.