On the basis of harmonic diffractive element theory and zoom theory, a dual-band and dual-field infrared optical system employing harmonic diffractive element is designed. The optical configuration is based on the axial motion of a lens group along the optical axis for changing field of view. The image quality evaluation are listed. Evaluation results show that the system has five lens and realizes a zoom of 40~80 mm in dual-band, which satisfing 100% cold shield efficiency. The modulaiton transform function value is over 0.5 at the Nyquist frequency for the waveband of 3.7~4.3 μm and over 0.3 at the Nyquist frequency for the waveband of 8.7~11 μm. The system is characterized by dual-band, high resolution, miniaturization and simple structure.