With the development of telecommunications and its applications, the design of compact antennas with high performance has become a great necessity. Among the important requirements is a high gain. In this article, a microstrip patch antenna using near zero-index metamaterial (NZIM) is proposed. This prototype is designed with the designing parameters of a rectangular microstrip patch antenna. The substrate material is FR-4. Simulation results show that this antenna operates at 5.8 GHz for a wireless local area network (WLAN). The proposed single antenna element achieves side-lobe suppression better than -13 dB. The 4×4 proposed antenna array is designed using 16 single elements and a T-shaped power divider to split power for each element. By covering a single-layer NZIM coating with a 4×4 array over a microstrip antenna, a gain enhancement of 14 dB is achieved in comparison with the single element. Over the operating band, the antenna prototype demonstrates steady radiation patterns. These characteristics are in good agreement with the simulations, rendering the antenna a good candidate for 5G applications. These antennas are designed, optimized, and simulated using CSTMWS2020.