A dual-band infrared optical system working in both mid-wave infrared (MWIR) (3~5 μm) and long-wave infrared (LWIR) (8~14 μm) has been designed with the double-layer Kinoform diffractive optical elements (DOEs). The system is comprised of four lenses , two ZnS lenses and two ZnSe lenses, and its focal length is 100 mm with F number of 1.2. The average efficiency of double-layer DOEs made of ZnS and ZnSe is more than 96%. The aberration of the system has been improved perfectly. When the Nyquist frequency is less than 14.3 lp/mm, the modulation transfer function (MTF) in MWIR is more than 0.7, which approaches to the diffraction limit. The MTF in LWIR is more than 0.65 in the same frequency. The effect of the efficiency for the MTF has been analysed. Due to the high diffraction efficiency, efficiency is not the main effect element for the performance of the system. A figure generated by the Matlab software shows the curves of the profile of DOEs. The blazed depths of the two kinoform surface have been calculated by the same software, which is 179.3 μm amd 159.4 μm, respectivly. The minimum feature size of the DOEs is 1.41 mm. It can be manufactured by the single-point diamond tuning (SPDT) technology easily and precisely.