To further increase the beam-wave conversion efficiency, a super klystron-like relativistic backward wave oscillator (RBWO) with coaxial-premodulation (CPM) cavity is proposed. Compared with previous dual-premodulation (DPM) cavities, the CPM cavity intensifies the second and the third harmonic components, resulting in a larger fundamental harmonic current both in the slow-wave structure (SWS) and the extraction cavity, and, consequently, leads to an enhanced microwave power generation by the Cherenkov radiation and transition radiation. In the particle-in-cell simulation, an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textit{X}$</tex-math> </inline-formula> -band microwave with a power of 3.44 GW and record efficiency of up to 80% has been achieved.