New applications for high-power microwave (HPM) have aroused the intense interest in the development of HPM sources. The relativistic backward wave oscillator (RBWO), as one of the most promising HPM sources, has proved to be a competitive candidate for generating multi-gigawatt HPM at L, S, C, and X-band. But for the conventional RBWO, in order to maintain high conversion efficiency, a high enough magnetic field is required to confine the intense relativistic electron beam. Obviously, it can lead to high energy consumption and bulkiness. Therefore, to fulfill the requirements for applications, enhancing the conversion efficiency of the RBWO at low magnetic field has received much attention and has been investigated extensively.In this paper, we present a well-designed RBWO model with a cavity-chain modulator and a TM₀₂ mode extractor to enhance the conversion efficiency at a low guiding magnetic field. The operation characteristics of the device are investigated in detail in this paper. Moreover, the function of each part of the device for enhancing the conversion efficiency is confirmed by the particle-in-cell simulation. In the device, the cavity-chain modulator is introduced to strengthen the beam bunching process. The TM₀₂ extractor after the modulator increases the Q-factor of the RBWO due to its partial reflection to the outgoing microwave. The increase of the Q-factor can enhance the standing electric field in the extractor. If the phase is appropriate, the extractor can convert the kinetic beam power into the RF power efficiently. The drift tubes between the reflector, the modulator and the extractor are used to adjust the bunching phase and the conversion phase of the modulated electron beam in the RF field. Moreover, an S-band high efficiency RBWO is designed and verified by the particle-in-cell simulation. An output power of 4.2 GW at a frequency of 2.38 GHz is obtained in the simulation. And the conversion efficiency reaches 50% when the guiding magnetic field is 0.7 T.