The principle and design method of employing diffractive optical element to athermalize an infrared optical system are discussed. An analysis is made on the diffractive optical elements dispersion characteristics and its superiority in correcting the second spectrum. A hybrid infrared optical system，as a practical application example，which has realized apochromatism and works beyond normal temperature, is presented. The parameters of the system are as follows: the focal length is 100mm，relative aperture is 1/2，field of view is 6°，and the working waveband is 8—11μm. In the system，only two materials，namely silicon and germanium, are used. The image quality of the system achieves the diffractive limit within the temperature range of -80—200℃. At about 0.7 aperture，three longitudinal aberration curves of the system intersect at one point，and the apochromatism of the optical system is achieved.