For the optical system with long focal length, the large relative aperture means that the imaging brightness is better, but it is difficult to correct with the variation of aperture edge aberration as well. The refractive system was used to reduce the total length of the optical system. Based on the reflection structure, the optical system was composed of two sets of correcting lens before and after, and the telephoto optical system with large relative aperture and short total length was effectively designed. The operating band of the optical system is the visible band, the focal length is 1 000 mm, the F number is 2.1, the telephoto ratio is 0.52, the optical total length is less than the focal length, the obstruction ratio is 45%, the full-field MTF is greater than 0.3 at the space frequency 80 lp/mm, and the image plane diameter is 11 mm. All the lenses of this optical system are spherical mirrors, and the system is composed of two reflectors and seven transmission mirrors, with compact structure and good imaging quality. The tolerance analysis of telephoto objective lens shows that the tolerance is good.