A relativistic backward wave oscillator for directly generating TE11 mode is proposed. An axially asymmetric slow wave structure and a sectioned annular cathode are introduced to suppress the TM01 mode and excite the TE11 mode. A pre-modulation dual-cavity, which allows part of the backward power to propagate into the diode region, is adopted to optimize the electron beam bunch, indicating that the conventional design principle that the diode region and the beam-wave interaction region should be isolated can be broken to increase the interaction efficiency. Particle-in-cell simulations show that when the diode voltage is 780 kV, and beam current is 6.1 kA, a microwave with power of 2.0 GW, and frequency of 9.25 GHz can be obtained, corresponding to an efficiency of 42%. Furthermore, the main output mode is TE11 mode, and the power of the cross-polarized mode is less than 10% within the calculation time of 50 ns.