The influences of infrared optical system structure parameters, which caused by temperature change, was analyzed. And the condition of infrared optical system athermal design was provided. Then, the temperature characteristic of diffractive optical element was discussed, and it was introduced into infrared optical system athermal design. A long-wave infrared optical system with hybrid refractive/ diffractive was designed by ZEMAX. The system was composed of three lenses, which used only two materials of Ge and ZnS, including five spherical surfaces and a diffractive surface. Its operating band was 8 to 12 μm, the filed of vision angle was 10.2°, the focal length was 45 mm, the F/number was 1.5 and the total length was 70 mm.The design result shows that the image quality of the system can approach the diffraction limit at the working temperature of -40 ℃ to 60 ℃. The modulation transfer function(MTF) is greater than 0.6 in the full filed of vision when the Nyquist frequency of detector is 20 lp/mm, and 87% of the energy is focused in single pixel. The imaging quality of the system is good, and athermal design is realized. The optical system has many advantages, such as compact structure, small volume, light weight and so on. It can be applied to martial or special infrared system.