Abstract: A C-band and X-band dual-frequency coaxial relativistic backward-wave oscillator (CRBWO) with an asymmetric resonant reflector and a single annular electron beam structure is designed and investigated in this paper. The improved slow wave structure (SWS) with stepwise variable coupling impedance is employed, and the particle-in-cell (PIC) simulation code is used to investigate the device. The PIC simulation results indicate that the axial electric field in the SWS is enhanced and the energy scatter of the relativistic electron beam (REB) is improved. With an electron beam of 511 kV and 8.95 kA and an axial magnetic field of 0.73 T, an average power of 1.0 GW with power conversion efficiency of 21.9% is obtained and the two dominant frequencies are 8.09 GHz and 9.91 GHz. The efficiency is higher than dual-band non-coaxial RBWO and other dual-band high-power microwave (HPM) generators. A more clear and stable beat radiation microwave power with beat frequency of 1.82 GHz is acquired, and the dual frequencies both demonstrate periodic-like dependence on the length of the tapered waveguide between the two SWS sections.