As a kind of high power microwave generator, the plasma relativistic microwave generators (PRMGs) have the virtues of wideband high power microwave output and fine frequency tunability. Thus PRMG is very useful for a wide variety of applications. The beam-wave interaction region in the PRMG is generally a cylindrical metal waveguide with preformed annular plasma. The dispersion characteristics of the operating slow plasma wave TM₀₁ mode (called as P-TM₀₁ mode below) in the interaction region are critical to the output properties. Therefore, the dispersion characteristics and field distributions of the P-TM₀₁ mode in a cylindrical waveguide loaded with annular plasma beam is studied numerically using the all electromagnetic PIC (Particle-in-Cell) code. Variation trends of the dispersion characteristics and the field distributions of the P-TM₀₁ mode with the density n_p, radial thickness Δr_p and radial position r_p of the plasma beam, the intensity of the guiding magnetic field B_z and the radius of the waveguide r_w are obtained. Simulation results show that: (1) Both n_p and Δr_p affect the dispersion characteristics markedly and the frequency of the P-TM₀₁ mode increases with the increasing of either n_p or Δr_p at the same axial wave number k_z. (2) Variations of r_p, r_w or B_z have very slight influence on the dispersion in the interested range. It is indicated that one can choose relatively larger dimensions of the waveguide for larger power capacity and lower guiding magnetic field for compactness if necessary. (3) The basic features of the field distributions of the P-TM₀₁ mode will not change with the variations of the above mentioned physical parameters. But with the increasing of axial mode number and k_z, the electromagnetic energy will be trapped inside the plasma beam gradually and no effective beam-wave interaction will happen in the end. Therefore, it is suggested to choose the operating point with relatively small k_z for the efficient operation of PRMG.