Abstract: The orthodox method for designing gradient refractive index lens requires that the feeding antenna possesses a steady phase center, which restricts the application of this lens. To break through the restriction, the paper presents a numerical method. By sampling the polarized electric field of the feeding antenna, phases of the electric field are got. Then they are used to design the gradient refractive index lens, which is fabricated from metamaterials with cut-wires structure. The design method is straightforward and flexible, with no restriction on the feeding antenna. Taking patch antenna as demonstration, the return losses and radiation patterns of the patch antenna and the lens antenna are compared. The data show that the lens obviously improves the gain and efficiency of the patch antenna. The gain is improved by 2 dB and the efficiency is increased from 62% to 99%.