The electromagnetic characteristics of the model with an electric line source radiating in the direction parallel to a lossy metamaterial covered infinitely long dielectric circular cylinder have been investigated. Firstly, the electromagnetic model is presented and the exact solution is derived. Secondly, this exact solution is employed in numerical calculations. The patterns of the near field under different electromagnetic parameters are obtained. The characteristics of the far field properties are also studied through the directivity and the normalized radiation resistance. Due to the effect of the negative refraction and the loss of the lossy metamaterial, in comparing the lossless metamaterial layer and the lossy conventional material layer, very different electromagnetic characteristics on the near and the far field of the lossy metamaterial covered dielectric cylinder are revealed.