By use of the self-consistent linear field theory, three-dimensional perturbation of electrons　affected by the perturbed electromagnetic fields is discussed. And Cherenkov radiations excited by a thin annular relativistic electron beam in a unmagnetized-plasma-filled, dielectric lined slow-wave waveguide are analysed. The dispersion equation and the wave growth rate of the interaction of the electron beam to the waveguide modes with arbitrary azimuthal mode number are derived. It′s clearly shown that the Cherenkov radiation results from the coupling of the waveguide mode in the unmagnetized-plasma-filled, dielectric lined slow-wave waveguide to the beam mode via the electron beam. Finally, the effects of plasma density on the dispersion relation and the wave growth rate are calculated and discussed.