In this paper, a novel and simple design of dual-stop-band frequency selective surface (FSS) for infrared stealth applications is investigated. The designed structure consists of three layers, metallic four multiplexed cross resonators located at the front and metal well structure at the back separated by a dielectric layer. The simulated results show that the proposed dual-stop-band FSS has high reflectivity in the two atmospheric windows (3.0-5.0μm and 8.0-14.0μm) for normal incidence waves, and the transmissvity is suppressed completely under 0.1. The effects of incident angle, polarization angle, period size and dielectric thickness on reflectivity and transmittance were investigated. the proposed structure also shows good transmission stability in a wide range of incident angles θ for both TE and TM incidences at azimuthal angle φ = 0°. Moreover, we demonstrate that such structure has good transmission stability for a wide range of azimuthal angles due to four-fold rotational symmetry of the designed unit cell. The principle of the resonant the proposed structure is formed not only by the electric resonance but also by the magnetic resonance.