The electromagnetic characteristics of the model for an electric line source radiating parallel to a lossless metamaterial covered infinitely long conductor circular cylinder is investigated. First, the electromagnetic model is presented and exact solution is derived. Second, the exact solution is employed in numerical calculations. The figures of the near field under different geometric and electromagnetic parameters are obtained; the characteristics of the far field properties are also studied through the directivity and normalized radiation resistance. Because of the negative refraction of the metamaterial, the distinct “focus”, which could not be seen in the conventional material, could be obtained in the material layer from the near field pattern. The presented electromagnetic model is compared with the former approach and its validity is proven.