The degradation of imaging quality of an infrared optical system is caused by the changing of environment temperature. Based on the differences in optical material thermal characteristics, a design method of long-wavelength infrared telephoto objective with optical temperature compensation is researched. Firstly, equations containing parameters are established according to the basic structure of telephoto objective and telephoto ratio. And then, the former group is complicated with different material combinations and the equations of athermal and achromatic to obtain initial optical power distribution. Finally, ZEMAX optical design software is used to optimize and correct aberration. Parameters of the design example are obtained such as 100 mm focal length, 2.0 F number, 0.8 telephoto ratio and 6° field of view (FOV). The result shows that the system has stable imaging quality in -40~60 ℃ operation temperature range, focal length variation is less than minimum depth of focus of the system and imaging quality approaches diffraction limit.