Gradient-index (GRIN) lens antennas leverage spatially varying refractive structures to generate high directivity beams. The lens antennas have the advantages of low loss, low power consumption and wide bandwidth over other kinds of high-directivity antennas, among which the low-profile flat GRIN lens antenna is compelling in millimeter-wave (MMW) 5G and satellite communication applications. The proposed 40 GHz GRIN metamaterial in this thesis is based on printed circuit board (PCB) technology, with relatively low cost compared with other fabrication methods such as layered dielectrics and perforated dielectrics. Besides, the proposed unit-cell design also has low-dispersion characteristics, allowing the wideband operation of the GRIN lens. We address the unit-cell characterization and homogenization by the Nicolson-Ross-Weir (NRW) method, and the measurement results exhibit good agreement with the simulation. Finally, a test GRIN lens is designed, simulated and measured in Ka-band.