Cherenkov radiation produced by a thin annular relativistic electron beam in aplasma-filled dielectric-lined waveguide is analysed by use of the self-consistent linear field theory considering the electron three-dimensional perturbation. The effect of the thin annular electronbeam on the beam-wave interaction is completely described by a jump condition. The dispersion equation and the simultaneous condition of the beam-wave interaction are derived. Finally
thegrowth rate of the wave is obtained
and the effect of the background plasma density and electronbeam radius on the growth of the wave are presented.