In this thesis, the properties of the metamaterials are studied. We analyze and discuss the artificial structure called metamaterials. The the effects on the radiation pattern and antenna gain are discussed when the structure is placed above the antenna. First, the propagation of electromagnetic wave in metamaterials is discussed. The metamaterial composed of metal rod array and split-ring is introduced. Next, the effects on permittivity, permeability and refraction index are studied when the structure parameters are changing. Thirdly, according to the above-mentioned summary, we use the structures to achieve an antenna radome. The radome can reduce 3 dB beam-width by about 31.25 percent at 10.75 GHz. The maximum gain achieves 7.25 dBi. In the fourth part, we also discusse the method of reducing the frequency band where negative refraction index occurs. The metamaterial is used to be a radome at the lower frequency band. The maximum gain is about 7.87 dBi. The 3 dB beam-width reduces by about 37.25 percent by the radome structure. Fifthly, the methods of improving the bandwidth are discussed when the antenna radome over the antenna . The enhancement of the antenna performance can be applied to the point-to-point communication. It also can save the cost of the feed network and the numbers of array antenna.