Abstract: The dispersion relations of a planar dielectric waveguide used in Cerenkov free-electron lasers are derived out and the existence of a group of odd modes, which can be simultaneously excited with the previously considered even modes, is reported. Discussion on the dependence of the radiation frequency and single-pass gain on the system parameters, the dielectric thickness, the beam energy and the beam channel width, is presented and the effects of the odd modes on the Cerenkov free-electron laser operation are investigated.