One of the difficult problems in optical manufacturing is to process and test large aperture and high-order aspheric surface. The spherical aberration coefficient of a high-order aspheric concave mirror with an effective aperture of 900 mm and a radius of curvature of 2580 mm was derived. Based on third-order aberration theory, the normal aberration of the high-order aspheric surface was compensated, and the initial structure of the compensation system was solved. Compensation systems based on spherical wave and plane wave were designed respectively, and the high-order aspheric concave mirrors were polished. The accuracy of the surface shape measured by four-dimensional interferometer is 0.022λ which meets the actual measurement requirements.