In this paper, a near-zero-index metamaterial is proposed by the composite I-shaped unit cell and the refraction index of this metamaterial is close to zero from 6.12GHz to 6.19 GHz. To study the characteristics and application of this near-zero-index metamaterial, especially the ability of focusing energy, a microstrip antenna is designed. According to the formulations for designing microstrip patch antenna, the conventional microstrip antenna, which resonance at 6.19GHz, is designed and optimized. This metamaterial is placed right above the conventional microstrip antenna and this system is tested by the finite element method (FEM). Simulation results show that the maximum radiation gain in H-plane of the microstrip antenna with this near-zero-index metamaterial is 9.24dB, while the maximum radiation gain in H-plane of the conventional microstrip antenna is 2.63dB, improving about 6.61dB than conventional microstrip antenna; the maximum radiation gain in E-plane of the microstrip antenna with this near-zero-index metamaterial is 9.24dB, while the maximum radiation gain in E-plane of the conventional microstrip antenna is 5.12dB, improving about 4.12dB than conventional microstrip antenna. Simulation results also show that the directivity of the microstrip antenna with this near-zero-index metamaterial is much higher, compared with the conventional microstrip antenna. Radiation gain at other frequencies, from 6.12GHz to 6.19GHz, is also obtained, the value is much higher than the conventional microstrip antenna at the corresponding frequency. The results indicate that near-zero-index metamaterials can improve the radiation gain and the directivity of the conventional microstrip antenna.