Abstract: A catadioptric cooled medium-wave infrared optical system was designed to solve the problems of large volume, weight, and cost of long focal length in large-aperture infrared imaging systems. First, a theoretical analysis and physical modeling were performed on the imaging principle of a coaxial two-mirror catadioptric medium-wave infrared optical system to achieve compactness and a low light-blocking coefficient. Subsequently, based on the light-blocking coefficient, the distance between the primary and secondary mirrors, position of the primary imaging plane, structural parameters of the primary mirror, secondary mirror, and secondary imaging group were calculated for the initial structure of the optical system. Finally, using optical design software 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 prepared for the joint optimization design. The system had an aperture of 310 mm, a total length of 320 mm, and a light-blocking coefficient of 0.26. At the Nyquist frequency of 42 lp/mm, the modulation transfer function (MTF) values across the full field of view were all greater than 0.35. Tolerance analysis showed that the system had excellent imaging quality and met 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.