Abstract: By use of the self-consistent linear field theory, 3D perturbation of electrons affected by the perturbed electromagnetic fields is generally discussed. And Cherenkov radiations excited by a thin annular relativistic electron beam and a solid relativistic electron beam in a plasma-filled, dielectric lined slow-wave waveguide are analysed in detail, respectively. The dispersion equations of the beam-wave interaction are derived. It抯 clearly shown that the beam-wave interaction results from the coupling of the TM mode in the plasma-filled, dielectric lined slow-wave waveguide to the beam mode via the electron beam. Finally, the growth rates of wave are obtained, and the effect of plasma density and the electron beam radius on the growth rate of the wave is calculated and discussed.