Efficient generation regime with a high power output has been experimentally realized in a klystron-like relativistic backward wave oscillator, in which a modulation cavity is inserted between the slow wave structure to decrease the energy spread of modulated beam electrons, and an extraction cavity is employed at the end of the slow wave structure to further recover energy from the electron beam. At a guiding magnetic field of 2.2 T, a microwave pulse with power of 6.5 GW, frequency of 4.26 GHz, pulse duration of 38 ns, and efficiency of 36% was generated when the diode voltage was 1.1 MV, and diode current was 16.4 kA. When the diode voltage was 820 kV, efficiency up to 47% with microwave power 4.4 GW was also realized experimentally.