Using the method of separation of variables in the elliptical coordinate system,the approximate eigenequation for an elliptical optical waveguide made from LHM is given. To find the propagation characteristics of fundamental mode in the elliptical optical waveguide,numerical methods are applied.Numerical examples reveal the influences of the permittivity,permeability of LHM and the eccentricity of the elliptical optical waveguide made from LHM on the fundamental mode propagation characteristics.These results show that the propagation characteristic of fundamental modes in the elliptical optical waveguide is influenced weakly by the permittivity and permeability of LHM and influenced strongly by the eccentricity of the elliptical optical waveguide. In addition,fundamental mode propagation characteristics in an elliptical optical waveguide made from LHM are compared with fundamental mode propagation characteristics in an elliptical optical waveguide made from RHM.