A novel filtenna-filter-filtenna (FA-F-FA)-based frequency-selective surface (FSS) technique is proposed using multiple-mode resonators (MMRs). Based on this method, a bandpass FSS with simultaneous wide passband and wide out-of-band rejection is validated. The MMR unit cell consists of two back-to-back magnetoelectric (ME)-dipole antennas and a filter-embedded GND plane. Four modes are analyzed and used to acquire a wide passband of the FSS. At the same time, wide out-of-band rejections in both lower and upper bands are controlled by the filter-embedded GND plane with four rotationally symmetric quarter-wavelength transmission lines (QWTLs). Moreover, the GND plane plays a crucial role in the impedance matching of the proposed FSS. As a result, four transmission poles (TPs) and three transmission zeros (TZs) of the proposed FSS can be obtained, leading to a fourth-order filtering response and wide out-of-band rejection. An equivalent circuit model, current distributions, and electric field distributions are introduced to illustrate the working mechanism of the FSS. Finally, the proposed FA-F-FA-based FSS with a 50.2% 3-dB fractional bandwidth (FBW 3 dB) in the passband and 53.5% and 119.2% of the 20-dB fractional bandwidth (FBW 20 dB), respectively, in the lower and upper rejection bands is achieved. The S-parameters are stable under an oblique incident angle of 50°. The measured and simulated results are in good agreement. In addition, the proposed FSS has the advantages of low profile, assembly free, and dual-polarization application, which verify the versatility of the FA-F-FA-based MMR FSS.