The electromagnetic properties of a composite structure with metallic wires in a Lorentz medium were studied. The results show that the electromagnetic properties of the medium host influence the plasma resonance of metallic wires and the left-handed character of the composite. The plasma frequency of metallic wires reduces with the rise of permittivity or permeability of the medium host. Also, the negative permeability of the medium can destroy the wires’ plasma resonance and prevent the realization of left-handed properties. The high loss of medium permittivity or permeability also inhibits the metallic plasma resonance. The negative influence of the media host on the left-handed properties of the composite structure can be effectively reduced by proper structure design, such as introducing a nonmagnetic medium in the host or using an anisotropic medium. The electromagnetic properties of a composite structure with metallic wires in a Lorentz medium were studied. The results show that the electromagnetic properties of the medium host influence the plasma resonance of metallic wires and the left-handed character of the composite. The plasma frequency of metallic Also, the negative permeability of the medium can destroy the wires’ plasma resonance and prevent the realization of left-handed properties. The high loss of medium permittivity or permeability also inhibits the metallic plasma resonance. The negative influence of the media host on the left-handed properties of the composite structure can be substantially reduced by proper structure design, such as introducing a nonmagnetic medium in the host or using an anisotropic medium.