Abstract: According to the surface temperature of military vehicles and for the infrared atmospheric window, a compound coating having photonic crystal structure was designed using common Si and LiF as the medium and in consideration of the respective dispersion relations. The calculation using the transfer matrix method showed when the two medium are of 4 layers respectively, with geometric thickness of each layer is 0.800 m and 1.900 m, there would be a strict band gap within 8-14 m, and the band gap had the following characteristics: With five or more medium layers, the band gap no longer changed substantially. When the geometric thickness of two medium increased, the band gap would have red shifts, width is wider and vice versa. The band gap between 8-14 m always exist regardless the changes of the incident angle. These conclusion may provide a useful reference for the experiment study of the coating.