Hybrid-mode horns such as corrugated horns, strip loaded horns and dielectric loaded horns have been used for satellite antennas due to their low cross-polarized radiation -. Furthermore, horns that support the balanced hybrid-mode can behave as either soft or hard horns, providing low sidelobes or high aperture efficiency -. Although corrugated horns have found wide use in satellite antennas, dielectric loaded horns are less desirable because of their higher mass, dielectric losses, and limited bandwidth. Recently, a metamaterial-based hybrid-mode horn design was proposed, where a metamaterial liner with dielectric constant less than unity was placed on the wall of the horn . It promises improved bandwidth as well as low manufacturing costs. In fact, metamaterials can exhibit a much broader range of electromagnetic properties, such as a negative or near zero index of refraction . In this work, a magneto-dielectric metamaterial liner with low refractive index was used to realize hybrid-mode horns. This paper provides metamaterial design principles and the expressions needed for hybrid-mode operation, as well as examples of conical horn antennas with metamaterial coatings that exhibit low cross-polarized radiation.