A dual-band frequency selective surface (FSS) with double screen was designed to cover the mid-infrared atmospheric window (3 μm~5 μm) and the far-infrared atmospheric window (8 μm~14 μm). This structure is composed of hexagonal metallic mesh and hexagonal resonant ring array. Simulation results show that the average transmission of FSS in atmospheric window is lower than 5%, and this structure is insensitive to the incident angle. The effect of the parameters on transmission properties was analyzed. The results show that adjusting the size of hexagonal ring structure can effectively adjust the -10 dB stopband bandwidth in 3 μm~5 μm, and increasing the size of metallic mesh can move the stopband in 8 μm~14 μm to long wave direction.