A structure for the design of dual-band dual-polarized quasi-elliptic frequency selective surfaces (FSSs) is proposed in this letter, whose unit cell is composed of multiple arrays of cylindrical dielectric resonators with capped annular ring resonators inserted in a perforated metallic plate. The designed FSS provides quasi-elliptic filtering responses with two transmission poles (TPs) in the passbands and two transmission zeros (TZs) in the upper stopbands. So does it for an incident wave with either TE- or TM-polarization in each band. In addition, the frequency responses including center frequencies, TPs/TZs, and the input impedance of the propagating path matched to the free space in each band can be tuned separately to achieve the best filtering performance.