In order to get the low transmission rate in both mid and far infrared atmospheric windows, an infrared frequency selective surface(FSS) composed of two layers based on hexagonal ring structure was designed. Simulation analysis using CST electromagnetic software shows that the frequency selective surface has two stopbands in both 3-5 μm and 8-14 μm, of which the average transmission is lower than 2.5%. Therefore, this frequency selective surface realizes two stopbands in infrared wavelengths; the filtering mechanism of the frequency selective surface was analyzed based on the method of surface current model analysis and the effective medium theory. And it was found that the inducted current on the surface of units was symmetrical in different resonance points, which enhanced the total scattering-field and led to the enhanced reflection. That was the ideal infrared stopband. The inducted current was produced by the coupling between screen and the coupling between unit in a screen; In the end, the effect of electromagnetic wave polarization mode, incident angle, dielectric layer properties and structural parameters on the transmission properties of the frequency selective surface was researched. The results reveal that the transmission of FSS is insensitive to polarization mode and incident angle, while the dielectric layer properties and structural parameters are important factors to the transmission.