This paper propose an X-band over-mode high-efficiency relativistic backward wave oscillator (RBWO), whose main structure includes a dual resonant cavity reflector, a periodic slow wave structure and an inserted coaxial mode selector. The RBWO uses an over-mode structure and transmits a pure TM₀₁ mode in the output waveguide. The dual-cavity reflector enables the slow-wave structure to achieve good isolation from the diode region under over-mode conditions, and at the same time provides sufficient pre-modulation for the electron beam to achieve high microwave conversion efficiency under low magnetic field. The addition of the coaxial inner conductor allows the device to work in TM₀₂ mode, while eliminating other unnecessary mode competition, achieving higher power capacity. In the PIC simulation, under the conditions of a guiding magnetic field of 0.63 T, a diode voltage of 850 kV, and a beam current of 11.74 kA, a microwave output power of 3.5 GW was obtained, and the device efficiency was about 35%.