The scattering of a plane electromagnetic wave by DNG metamaterial of semi-elliptic boss over a perfectly conducting ground plane is investigated. The scattered field is represented in terms of an infinite series of a complex radial and angular Mathieu functions with unknown expansion coefficients. The formulation is carried out using the boundary value solution along with the image theorem. The problem is replaced by a complete elliptic cylinder with no ground plane, and the given incident plane wave is supplemented by an image plane wave chosen such that the boundary condition for the total electric field is satisfied at all points where the conducting plane is located in the original problem. Scattering numerical results of the elliptical boss with lossy DNG metamaterials is compared with a conventional material and lossless DNG metamaterial.