Abstract: Based on a novel compact P-band coaxial relativistic backward wave oscillator(RBWO) with only three periods slow wave structure (SWS), an L-band coaxial RBWO is proposed and investigated. Particle simulation results show that, with the 591 kV, 8.2 kA electron beam guided by the 0.8 T solenoidal field, the microwave is generated with the power of 1.50 GW operating at about 1.64 GHz. The interaction efficiency is about 31% and the optimized size of SWS is only f96 mm207 mm. Furthermore, the electrodynamics characteristics of the proposed device, expressly the longitudinal resonant modes and quality factors, are analyzed. Finally, a principle of design for low-band coaxial RBWO is presented with the results of P-band coaxial RBWO and L-band coaxial RBWO, i.e., the length of SWS is about equal to the wavelength, the period length of SWS, and the depths of outer and inner conductor ripples are respectively about 5/13, 1/10, and 1/30 times the wavelength, the radius of electron beam is about 0.7 times the average radius of outer conductor ripple, the longitudinal resonant mode is 0.8 mode and the Q-factor is about 16.