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In the first part of this paper, we explain the basic concept of left-handed material and we will look at the history of implementing LHM materials at high frequency. In this part we have investigated the characterization process of metamaterials, the effective dielectric and magnetic properties are retrieved from the scattering parameters. Moreover, we provide a detailed study about the effective parameters such as the refractive index, permeability, permittivity and the group delay. For this purpose we have designed special LHMs that resonate in X-band frequency which is around 8GHz-12GHz. In the second part of this paper, a new topology for designing a circularly polarized 2 × 4 linear antenna array composed of circular Split Ring Resonator SRR for X-band is discussed. The design of metamaterial antenna array based Circular Split Ring Resonator operating at about 10.75 GHz and present a gain of 5.2 dB and the aperture at -3dB is 58°.