Optical features of optical system of a dual-band imaging spectrometer is analyzed.Based on the mutual compensation of optical materials focal plane shift constant, the equations are formulated for athermalization of optical system. A design example of a three lenses optical system with two materials operating in the 3～5 μm and 8～11 μm wavelength bands with 100% cold shield efficiency, 10° field of view, 100 mm focal length, 1.98 F number is designed, associated with high optical quality in large working temperature range -20～70°C. The defocus, wavefront error and modulation transfer function(MTF) of optical system are analyzed.