Coaxial relativistic backward wave oscillator with the rippled inner conductor not only increases the output efficiency but also results in the serious phenomenon of pulse shortening in experiments. Our research indicates that the two main mechanisms leading to the pulse shortening are the electron beam interruption and combining effects of the explosive field electron emission and the secondary electron multipactor on the surface of the slow-wave structure. In order to enhance its power capacity the electrodynamic structure is modified by detailed analysis of the field distribution in the coaxial slow-wave structure. The appropriate resonant reflector and the electron collector are developed for the application of the coaxial relativistic backward wave oscillator. A series of surface treatment is applied to enhance the power capacity of the coaxial RBWO. In the experiment, the microwave pulse duration is increased from less than 10 ns to 20 ns, and the output efficiency is enhanced from less than 20% to 34% employing the electron beam pulse of the full width at half maximum 28 ns. The peak power of 1.01 GW at the frequency of 7.4 GHz is achieved. It is found that the output efficiency of the coaxial RBWO is likely to be advanced if its power capacity can be boosted further.