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A novel frequency selective structure characterized with quasi-elliptic filtering response and broad bandwidth is presented. The new structure consists of a two-dimensional (2-D) periodic array of apertured cavities. A nearly 30% relative bandwidth and a bandwidth ratio of 1.13 are achieved with three resonances in reflection response. Relationships between geometry dimensions and responses are fully investigated with simulations. Meanwhile, the multilayered structure is proved to be a promising candidate for elliptic response. Furthermore, the theoretic analysis of the structure is provided in detail, which also reaches an agreement with the simulation result. This research is a meaningful reference in design and analysis of frequency selective structures.