Guided modes in a dielectric waveguide structure with a coaxial periodic multi-layer are investigated by using a matrix formula with Bessel functions. We show that guided modes exist in the structure, and that the field is confined in the core which consists of the optically thinner medium. The dispersion curves are discontinuous, so that the modes can exist only in particular wavelength bands corresponding to the stop bands of the periodic structure of the clad. It is possible that the waveguide structure can be applied to filters or optical fibers to reduce nonlinear effects.