The application of diffractive optical elements (DOEs) in infrared dual-band and even multi-band has become a hotspot. Based on the design idea of polychromatic integral diffraction efficiency (PIDE) maximization of the double-layer DOE, the optimal working wavelength is designed in the range of working band, and the optimal microstructure height of the double-layer DOE is calculated. The mathematical analytical model of weight distribution of PIDE of a multi-band optical system is proposed. Based on this double-layer DOE, a dual-band (3.7-4.8 μm and 8.0-12.0 μm) infrared optical system with an F-number of 1.1 and a focal length of 75 mm is designed. When the system is at a spatial frequency of 29.4 lp/mm, the modulation transfer functions of the designed system are above 0.60 and 0.45 for the medium wave infrared (MWIR) and long wave infrared (LWIR), respectively, and the designed optical system realizes athermalization over the temperature range from -40 ℃ to 60 ℃. The system has shown great advantages in improving image quality, miniaturization, lightweight, and athermalization in infrared dual-band.