This paper proposes a new low-profile high-gain wideband gradient refractive index (GRIN) lens fed by a magnetic-electric (ME) dipole antenna. As a constituent part of this lens, a novel sub-wavelength nonresonant metamaterial unit cell composed of 3-layer substrates is also proposed. By applying Rogers 5880 and air as the top and bottom layers, high and low refractive indexes can be achieved for realizing the core layer and impedance matching layer (IML), respectively. Therefore, the proposed lens antenna can exhibit high gain of 19 dBi and-10 dB bandwidth of 58% (6.8-12.4 GHz). Moreover, due to the high refractive index which is realized by the bilayer cross-shaped rings meta unit cell, the total thickness of the lens is 0.32 λ0, where λ0 is the wavelength at 10 GHz.