Zero-index meta-materials have been investigated extensively for their unique electro- magnetic properties. In order to achieve the miniaturization of high performance antenna, a kind of zero-index material is designed, i.e., metal-mesh structure, by adjusting the effective plasma frequency to the desired frequency band. The numerical simulations indicate that this metal-mesh structure can improve the wave-front phase and increase the gain when this structure is introduced to a horn antenna. The front wave phase of the antenna is changed from the spherical wave to the plane wave, the corresponding gain of the antenna is increased by at least 2 dB. The effect of the geometrical parameters, including the number of mesh layers n, the distance between adjacent layers h, the period a for a single mesh layer, and the radius of the metal lines r, are investigated systematically to optimize the directional emission.