In order to meet the multi-band and integration requirements of the communication apparatus, the coupling and resonance mechanism can be exploited to design a frequency selective surface (FSS), with two pass-bands at Ku-band and Ka-band, which is composed of three metallic layers and fabricated on a flat substrate equivalent to a solid wall radome or an A-sandwiched radome. According to the physical structure of the FSS, an equivalent circuit model is established to analyze the filtering mechanism, and the transmission characteristics of the radomes with FSS are obtained by using a full-wave analysis software. The first pass-band at Ku-band with miniaturization property can be achieved by coupling the electric and magnetic field of the three surfaces, while the second pass-band at Ka-band can be achieved by the resonance of the square loop slots embedded in the capacitive surfaces. The transmissions of the solid wall radome and A-sandwiched radome with FSS are 89% and 94.7% at Ku-band, and 88.2% and 93.7% at Ka-band, respectively. When the incident angle is varied from normal to 60°, the frequency response characteristics of the two pass-bands are stable. Finally, the experimental results of the prototype with a solid substrate measured in free-space environment are in good agreement with the simulated values. The proposed radome structure with FSS, which is based on the coupling and resonance mechanism, can achieve two stable pass-bands at Ku-/Ka-band. This may provide some theoretical and experimental assistance for the study of the multi-band and wide band spacing FSS.