A new band-reject frequency-selective surface (FSS) based on dual-band near-zero refractive index metamaterial (ZIM) design is presented in this paper. Consisting of a planar array of complementary dual-layer symmetry resonant ring, the proposed FSS exhibits a high-selective band-reject filtering response. From the viewpoint of effective medium, the subwavelength FSS is characterized by near-zero effective magnetic permeability and near-zero effective electric permittivity in two different operational bands, respectively. The corresponding resonant behavior and E-field distributions are analyzed in detail. A prototype of the proposed FSS working in X-band is fabricated and measured. The simulation and experiment results verify the effectiveness and correctness of the ZIM-based design method.