In order to realize double-band properties of frequency selective surface (FSS), the composite element FSS, composed of rectangle grid and three-ring loop element, is presented. The spectral domain solution method is described in detail for FSS. The frequency response properties of FSS are analyzed for electromagnetic waves with different incident angles and polarizations based on the spectral domain method. The result shows that the designed FSS can maintain stable double-band, flat top transmission and sharp skirt properties for electromagnetic waves with different incidence angles and polarizations. The double-band properties show stop-band from 1.8 GHz to 5.4 GHz and pass-band from 5.4 GHz to 20.0 GHz. The resonant frequency of stop-band is situated at about 3.1 GHz, and the bandwidth of flat top transmission is over 14.3 GHz at -4 dB. The sharp skirt properties show that the S-band signal is reflected intensively and other band signals are transmitted, and multi-band communication is achieved. The composite FSS can be used in satellite communications, radomes and other fields.