An imaging optical system with large relative aperture and field of view was designed based on a modified Mangin mirror. The aberrations of the modified Mangin mirror are analyzed and a design method is proposed for it. The optical system adopts a combination of an improved Mangin mirror and a catadioptric optical system. The relative aperture is 1/1.8, field of view is 4°× 4°, working band is 450-850 nm, and focal length is 380 mm. The imaging detector is a CMOS detector with pixel of 2 μm×2 μm. The modulation transfer function value is close to the diffraction limit and greater than 0.5 at a Nyquist frequency of 250 lp/mm. The secondary mirror of the system is designed based on a Mangin mirror and an achromatic lens. Based on the spherical aberration and sine aberration obtained from the preliminary optimization analysis of the initial system structure, the focal power of the achromatic Mangin mirror is solved by the PW method. Based on achromatic conditions and residual chromatic aberration of the system, the focal powers of three surfaces of the achromatic Mangin mirror are solved and the radii of the surfaces can be calculated. The system has small monochromatic and chromatic aberrations and good imaging quality.