According to technical requirements and the structure characteristics of long-focal-length optical system, the paper analyzes the advantages and shortcomings of reflective system and refractive system in details. By the aberration theory and ZEMAX optical design software, a long-focal-length space optical system which is characterized by the catadioptric configuration, with the spectrum band 500 similar to 800 nm is designed. And evaluations show that the image quality is close to the diffraction limit. After being manufactured, the optical transfer function (simplified MTF) of long-focal-length lens is tested, and it shows that the best focal planes of spectrum 500nm similar to 800nm, 550 nm, 650nm are not in the same position and deviate greatly, which is chromatic aberration. Whereas, after remeasuring the long-focal-length lens, it is found that the MTF values of the three wavebands can meet the qualification requirements simultaneously if we defocus 57.7 mu m from the best focal plane of spectrum 500nm similar to 800nm. Finally, the cause of chromatic aberration phenomenon in the measurement of catadioptric optical system is deeply discussed at the first time based on the structure characteristics of optical system, then the improvement is achieved correspondingly and the results show as below: the full-aperture spherochromatic aberration of improved optical system is reduced from 0.45 mu m to 0.25 mu m, and its MTF values are up to 0.6 plus. The technical requirements of high-precision, small size, light weight, good image quality are fulfilled.