Abstract: Based on the working principle of the backward wave oscillator (BWO) with a low magnetic field, a frequency-agile relativistic backward wave oscillator (RBWO), whose frequency can be counterchanged between X band and C band by changing the strength of the guiding magnetic field, is designed. To actualize frequencys agile counterchange, two sections of slow wave structure (SWS), whose appeals on parameters of electron beams are accordant, are linked. When the energy of the electron is 670 keV while the beam current is 8 kA, the simulated result of 1.0 GW output microwave power with 6.28 GHz frequency is obtained on conduction of 0.5 T guiding magnetic field, while 0.75 GW output microwave power with 9.26 GHz frequency is obtained on conduction of 0.8 T guiding magnetic field.