Military infrared detection technology mainly focuses on the infrared radiation of target in mid-infrared atmospheric window (3 μm~5 μm) and the far-infrared atmospheric window (8 μm~14 μm), therefore reducing the infrared transmittance of the target in these two atmospherics can effectively decrease the possibility of detection. Frequency selective surface (FSS) has good spatial filtering characteristics and can be used to suppress the infrared transmit-tance of the target in the band of interest. In order to extend the bandwidth of FSS and realize multi-band selection, we combine hexagonal ring structure with hexagonal metal mesh. Meanwhile, we adopt double layers to further ex-pand the bandwidth. Simulation results show that the infrared transmission of the structure is lower than 5% in 3 μm~5 μm and 8 μm ~14 μm. The structure realizes the suppression of infrared transmission in mid-infrared atmos-pheric window and far-infrared atmospheric window. The absorption of the structure is nearly 10% in 3 μm~5 μm and 8 μm~14 μm, which indicates the low infrared radiation of the structure. Moreover, the reflection of the FSS is close to 90%, which suggests that the stopband characteristic of the structure is mainly due to the reflection en-hancement caused by the scattering field produced by the surface current. The surface current distributions at 4 μm and 10 μm show that the stopband characteristics at 4 μm is mainly caused by the scattering field produced by the surface current of hexagonal ring structure, while the stopband characteristics at 10 μm is mainly caused by the scattering field produced by the surface current of hexagonal metal mesh. The structure is insensitive to polarization. At oblique incidence, the structure can still maintain low infrared transmittance in 3 μm~5 μm and 8 μm~14 μm. When the line width w decreases from 0.25 μm to 0.10 μm, the equivalent size of the hexagonal metal mesh increas-es and the spacing of the hexagonal ring structure units decreases, which causes the transmission curve moves to-wards the long wave and the -10 dB bandwidth in 3 μm~5 μm increases from 2.47 μm to 3.08 μm. When L1 reduces from 0.75 μm to 0.60 μm, the spacing of the hexagonal ring structure units increases, which weakens the coupling effect between the units, and the -10 dB bandwidth in 3 μm~5 μm reduces from 2.92 μm to 1.65 μm, meanwhile grating lobe appears in 3 μm~5 μm. When L2 changes from 0.85 μm to 1 μm, the transmission curve in 8 μm~14 μm moves towards long wave due to the increase of equivalent size of the hexagonal metal mesh.