The study of optical waveguide geodesic lenses free of aberration and singularity in curvature is reported. In profile design of geodesic lenses, a suitable function of generating line in transitional zone that quotes from Ref.[1] can eliminate effectively the curvature singularity of rounded-edge of lenses. This kind of geodesic lenses are designed and fabricated. The experimental measurements show that geodesic lenses eliminated the spherical aberration in the range of 8 mm effective aperture and obtained the diffractive spot of 3.3 μm size for input beam of 4.78 mm width.