A periodic structure frequency selective surface with gold film circular ring was designed base on finite element method. Simulation results show that the periodic structure has a obvious effect on infrared radiation suppression in far infrared atmospheric window (8～14 μm). The average transmittance is below 20% within 25～37.5 THz (8～12 μm),especially it is less than 10% within 27～36 THz. Influence rules of different structure parameters on the transmission characteristics are analyzed by optimizing calculation,such as radius,width and thickness of circular ring.