Using only three lenses, an infrared system matching 640×512 uncooled vanadium oxide long-wave focal plane detector was designed. The system has a focal length of 100 mm, an F-number of 1.1, a total length of 107 mm, and a working band range of 8-12 .m. A binary diffraction surface was introduced to realize the non-thermal temperature compensation function. The simulation design using Zemax shows that the modulation transfer function (MTF)value at the Nyquist frequency (30 lp/mm) of the system reached 0.49 in the temperature range of -40℃-+60℃, which is close to the diffraction limit. The system has the characteristics of a long focal length, large relative aperture, good image quality in the full field of view, suitable temperature adaptation, high binary diffraction efficiency, easy processing, and compact structure.