Temperature changes will have an impact on the imaging quality of the optical system， and this impact is particularly obvious in the infrared band. The changes of the optical system material’s refractive index， spherical curvature and other parameters affected by temperature are analyzed in this paper. According to the principle of optical passive athermalization，an infrared optical system with a working band of 3~5 μm， a focal length of 30 mm， and F#=4 is designed. The pixels of cooled detector are 640×512 and the single pixel is 15 μm. The system adopts a four-piece structure， using two common mid-wave infrared materials， silicon and germanium， to meet the requirements of athermalization and achromatic aberration. It can maintain excellent performance in the operating temperature range of -30~+60 ℃. The image quality meets the requirements of the refrigerated mid-wave infrared system.