The composite dielectric waveguides with multi-boundaries in radial directions have axially unsymmetrical structures. To have the large difference in propagation constant for the two orthogonal HE11 modes, the waveguides have attracted our attention as a new type of single-polarization optical fibers. In this paper, the modal characteristics of the composite dielectric waveguides are investigated by a numerical analysis based on the point-matching method. The dispersion characteristics for millimetric dielectric waveguides with large difference in dielectric constant as well as single polarization optical fibers with small difference in refractive index are shown. Also, the patterns of electric field distributions for propagating modes are illustrated. The propagation constants are obtained with three significant figures for both the dominant and higher order modes. Microwave model experiments using a composite dielectric waveguide made of Rexolite and Teflon were carried out to confirm the theory.