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In this paper, a high refractive index metamaterial (HRM), whose element is composed of bilayer square patch (BSP) spaced by a dielectric plate, is proposed. By reducing the thickness of the dielectric plate and the gap between adjacent patches, the BSP can effectively enhance capacitive coupling and simultaneously suppress diamagnetic response, which significantly increases the refractive index of the proposed metamaterial. Furthermore, the high refractive index region is far away from the resonant region of the metamaterial, resulting in broadband. Based on these characteristics of BSP, a gradient refractive index (GRIN) lens with thin thickness (0.34λ0, whereλ0 is the wavelength at 5.75 GHz) is designed. By using this lens, we then design a circularly polarized ho antenna with high performance. The measurement results show that the 3-dB axial ratio bandwidth is 34.8%(4.75 GHz~6.75 GHz) and the antenna gain in this frequency range is increased by an average value of 3.4 dB. The proposed method opens up a new avenue to design high-performance antenna.