The propagation of electromagnetic waves in an elliptical plasma waveguide including strongly magnetized plasma column and a dielectric rod is investigated. The dispersion relation of guided hybrid electromagnetic waves is obtained. Excitation of the waves by a thin annular relativistic elliptical electron beam will be studied. The time growth rate of electromagnetic waves is obtained. The effects of relative permittivity constant of dielectric rod, radius of dielectric rod, accelerating voltage, and current density of the annular elliptical beam on the growth rate and the frequency spectra are numerically presented.