A novel and simple design of dual-stop-band frequency selective surface(FSS) for infrared stealth applications is proposed and investigated. The proposed structure consists of three layers, metallic four multiplexed cross resonators as the front layer, metal well-shaped structure as the bottom layer and a dielectric layer as the separator. The simulated results show that the proposed dual-stop-band FSS has high reflectivity in the two atmospheric windows (3.0~5.0 μm and 8.0~14.0 μm) for normal incidence waves, and the transmissvity is suppressed completely below 0.1.The influence of incident angle, period size and dielectric thickness on reflection and transmission were investigated. The proposed structure also shows good transmission stability in a large incident angle θ for both TE and TM modes at azimuthal angle φ=0°. The stop-band principle of the proposed structure is formed not only by the electric resonance but also by the magnetic resonance.