With rapid growth of uncooled infrared detector technology, uncooled infrared optical systems are widely used. The uncooled infrared optical system must fulfill the requirements of compact size, large relative aperture, high temperature adaptability and stray light suppression ability. A catadioptric optical system with secondary image is adopted to realize the design parameters of 0.55 ratio of total length and focal length and 0.8 F number. In addition, the optical passive compensation method is used to realize an athermalized design in the temperature range of -40 ℃~50 ℃ by matching optical and structural materials properly, and the field stop in the first image can ensure the optical system a high stray light suppression ability. The design result shows that optical system′s modulation transfer function in each field is close to the diffraction limit at different temperatures and the system size is compact. Finally, it is proved that this uncooled infrared optical system can meet environmental requirements of airborne and missile application through the actual imaging experiment at high and low temperatures.