According to the requirements of good image quality, miniaturized dimension and high-temperature environmental adaptability in the applications of infrared search and track systems presently, a compact infrared catadioptric system structure is used, which base on the J-T cooler staring high-sensitivity focal plane array infrared detector comprised of 320×320 elements, to design a low F-number and compact athermalizing infrared system optical system. The ratio of total length and focal length is 0.6. A passive optical athermalization design is used for infrared optical systems, which makes the system athermalize in the temperature range of -40 ℃～60 ℃. The stray radiation in the system is also analyzed and a scheme to suppress the stray radiation is given. The results show that the modulation transfer function (MTF) (17 lp/mm) of optical system in all field of view approaches the diffraction limit at different temperature, and 80% energy concentrates in 1 pixel. The optical system has many advantages, such as compact structure, small volume and so on . It can meet requirement of imaging infrared search and track.