By making the best of the spectral information of medium and long infrareds, a harmonic diffractive/refractive optical system in middle and long infrareds is established, the hyper-spectral imaging system has obtained more than 200 spectral images in medium-wave infrared band of 3.7~4.8 μm and long-wave infrared band of 8.5~12 μm based on the special large dispersion capability of harmonic diffractive elements.The design results show that the optical modulation transfer function is greater than 0.52 at 18 lp/mm in medium-wave infrared band; and greater than 0.51 at 13 lp/mm in long-wave infrared band.Furthermore, the RMS spot diameter is less than 27 μm in medium-wave infrared band and is less than 34 μm in long-wave infrared band.Obtained data indicate that the optical modulation transfer functions at all wavelengths are close to the diffraction limit; and the RMS diameter of points can match with the pixel size of existing detectors.