A dual-band high-efficiency coaxial relativistic backward wave oscillator (CRBWO) with asymmetric resonant reflector is designed and presented in this paper. Improved sectioned coaxial slow wave structure (SWS) with stepwise variation of coupling impedance and phase velocity is employed, and the performance of the dual-band CRBWO is investigated by use of a 2.5-D particle-in-cell (PIC) simulation code. When the diode voltage is 510 kV and beam current is 9.03 kA, an average microwave power of 1.0 GW with power conversion efficiency of 21.7% is obtained. Synchronously radiating dual-band frequencies of 8.1 GHz and 9.9 GHz are obtained, corresponding to C-band and X-band, respectively. A more clear and stable beating radiation microwave power with beating frequency of 1.8 GHz is acquired.