With a resonant cavity inserted between the second slow-wave-structure section and the tapered waveguide, a new structure of the multiwave Cerenkov generator (MWCG) operating at low guiding magnetic field is proposed to produce high efficiency and high power microwave. Some features and potential advantages of the proposed device are analysed. The 2.5-dimensional particle-in-cell simulation is employed to verify the initial expectation.The results show that, with the use of an electron beam of 640kev and 8.4kA guided by the magnetic field of 0.6 T, a stable and monochromatic X-band microwave output of 4 GW in peak power is achieved, and the average efficiency is over 30%.