A new type of slow-wave system (SWS) for the beam-wave interaction——putting a plasma column into a dielectric-partially-filled waveguide, is presented. By use of the linear self-consistent field theory, the interaction of a relativistic electron beam with the wave in the SWS is analysed. Determinative dispersion equations are derived for a thin annular relativistic electron beam propagating through the SWS surrounding and existing inside the plasma column, respectively. These dispersion equations are directly solved numerically, and the cut-off frequency, the operation frequency and the growth rate of the waves are obtained. Finally, the effects of the parameters of the plasma column on them are discussed.