This paper presents a low-profile and wideband metamaterial-lens (metalens) antenna based on high-refractive-index metasurface. A novel three-layer nonresonant metamaterial unit cell is introduced and analyzed by the full-wave simulation tool. The proposed unit cell is a stacking configuration of four H-shaped lines realized by multiple microwave laminates. It can achieve a large refractive index variation range of 4.76 (from 1.5 to 6.26). In addition, two impedance matching layers based on the proposed unit cell are developed to provide better transmission for incident waves passing through the metalens antenna. The attractiveness of this new metalens antenna is its low-profile thickness of <inline-formula> <tex-math notation="LaTeX">0.26~\lambda _{0} </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">\lambda _{0} </tex-math></inline-formula> is the wavelength at 10 GHz. To validate the performance of the metalens antenna, a wideband stub-loaded horn antenna with stable radiation patterns in E- and H-planes is adopted as the feeding antenna source. The measured results demonstrate a wide impedance bandwidth of 66% (7.2-14.3 GHz) and a high aperture efficiency of up to 65%. Moreover, its sidelobe and cross-polarization levels are less than −17 and −25 dB across the entire bandwidth, respectively.