The analysis model of comprehensive polychromatic integral diffraction efficiency (PIDE) of multilayer diffractive optical elements (MLDOEs) working within a range of incident angle was established. Based on the special characteristics of achromatism and athermalization of MLDOEs, an infrared dual-band optical system with double-layer DOEs working in the 3.7 μm~4.8 μm and 7.7 μm~9.5 μm wavebands was designed. The effective focal length of the optical system is 200 mm, and F # is 2. The cooled focal plane array is 320×256 and the pixel pitch is 30 μm. The MTF is higher than 0.66 and 0.54 at the frequency of 17 lp/mm for mid-wave infrared (MWIR) and long-wave infrared (LWIR), respectively. The maximal root-mean-square(RMS) radius is less than 11.702 μm, the wavefront error is smaller than 0.191 7λ and the maximal defocus is less than the focus depth, the designed optical system realizes athermalization over the temperature range from -55℃ to 71℃. The incident angle upon the diffractive surface is within the range of 0°~5.19°, the comprehensive PIDE of the double-layer DOEs are 99.81% and 97.36% for the MWIR and LWIR waveband, respectively. The structure of the designed infrared dual-band optical system with double-layer DOEs is simple with good image quality, can be used in military detection system.