A dual-passband frequency selective surface (FSS) is designed in this paper. Two passbands are 2-3.4 GHz and 5.5-6.8 GHz, respectively. It is used as a spatial filter to improve the radiation and scattering performance of an antenna. The structure is combined with two layers. One is metal, and the other is intermediate medium. The requirements of wide-band, polarization-independent, wide incidence angle and miniaturized FSS with a thickness of only 0.0085λ are achieved by parameter optimization. When the FSS is used to the proposed microstrip antenna, the relative bandwidth is increased by 31.4% and 50%, and the peak gain is increased by 2.53 dB and 1.86 dB at 5.8 GHz and 6.4 GHz, respectively. Meanwhile, the maximum RCS reduction of the microstrip antenna is 16 dB. On the other hand, the FSS is able to be applied to a dipole antenna to improve the transmission coefficient and phase. Simulation and measurement results of the transmission coefficient and phase of the antenna are almost the same.