On the basis of continuous polishing, a new polishing process was developed to meet the special requirements of ring lasers, synchrotron radiation accelerators and optical oscillators for the sphere mirrors with a large radius of curvature. Based on the Preston hypothesis, a mathematical model of material removal was established by analysis on the relative velocity at the radial point of an optical sphere surface in the classic polishing process. Via computer simulation, it explored that the reasons of the nonuniformity in sphere mirrors were that the mirrors cannot stay in the polishing pan during the polishing process and the rotation rate of the polishing pan is asynchronous with the mirrors. Two improvements were enlarging the size of the polishing pan and synchronizing the mirror rotation with the polishing pan. With the proposed process, a spherical mirror with the radius of 6 000 mm was polished. Obtained results show that the nonuniformity ΔR/R in a sphere is less than 0.02, the roughness is less than 0.25 nm and the surface defect reaches a zero grade.