Abstract: To solve the problems of large volume, weight, and cost of long focal length and large aperture infrared imaging systems, a catadioptric cooled medium-wave infrared optical system has been designed. Firstly, to achieve compactness and low light blocking coefficient, theoretical analysis and physical modeling were carried out on the imaging principle of a coaxial two mirror catadioptric medium-wave infrared optical system. Then, based on the light blocking coefficient, the distance between the primary and secondary mirrors, and the position of the primary imaging plane, the structural parameters of the primary mirror, secondary mirror, and secondary imaging group are calculated as the initial structure of the optical system. Finally, using optical design software for joint optimization design, a catadioptric cooled medium-wave infrared optical system with a focal length of -600 mm, F-number of 2, and imaging field of view of 0.59°×0.59° was completed. The aperture of the system is 310 mm, the total length is 320 mm, the light blocking coefficient is 0.26, and the modulation transfer function values of the full field of view are all greater than 0.35 at the Nyquist frequency of 42 lp/mm. Tolerance analysis shows that the system has excellent imaging quality and meets practical application requirements. This infrared optical system has broad application prospects in fields such as optical remote sensing satellites, electro-optical theodolites, and airborne electro-optical systems.