Based on the general analytical method of designing aspherical optical waveguide geodesic lens, the effect of rounded-edge on the curvature behavior of lens depression profile has been studied. It is pointed out that taking profile of continuous second derivative can eliminate the curvature singularity effectively and diminish the radiation loss of guided light due to waveguide bending. A new rounded-edge function has been presented by which the lens depression profile and the depth of lens can be obtained and comparison with the particular solution given by Sottini et al. is made.