Abstract: This paper studies a high efficiency X-band over-mode relativistic backward wave oscillator (RBWO), which is composed of a dual-cavity reflector, a 7-periods trapezoid SWS and extraction cavity. The ratio of D to λ of the generator is 2.6, and the electron beam interacts with the TM₀₁ near π mode of the structure wave. In the SWS region the TM₀₁ mode surface wave mainly transfers to the TM₀₂ mode body wave, the primary mode of the output microwave is TM₀₂ mode with the proportion 81%, and the remainder is TM₀₁ mode. A method to design the resonant reflector under over-mode condition is proposed, a dual-cylindrical cavity reflector is optimized by using the mode-matching method, and the reflection coefficients for the TM₀₁ and TM₀₂ modes are larger than 0.99, hence good insulation between the SWS and the diode is achieved. Simultaneously, the longitudinal electric field of the resonant reflector could pre-modulate the electron beam sufficiently, which would promote the beam-wave interaction in the SWS. Furthermore, the transfer coefficient is increased by loading the extraction cavity after the SWS. Simulation results indicate that microwave output power of 6.6 GW is achieved, the diode voltage is 900 kV and beam current is 14.3 kA, and the transfer efficiency is 51%.