The tunable capability expands the application fields of backward wave oscillator (BWO), especially for large range modulation. This paper presents analysis, PIC simulation, and preliminary design of a novel relativistic BWO which achieves the purpose of modulation among three or more frequencies within two bands. A new dielectric slow-wave structure (SWS) with hollow section was designed in the novel BWO instead of the conventional SWS with fixed solid conductors. The wide range of adjustment of propagation constant and output frequency could be easily achieved by modulating the concentration (permittivity) of the dielectric filled in the hollow section. The results of PIC simulation show the output has three stable situations at two bands with a magnetic field of 3T: 6.9 GHz, 0.9 GW; 7.3 GHz, 1.1 GW; and 10.0 GHz, 1 GW. The specific permittivities of the corresponding SWSs are 15.7, 34.3, and 42.0, respectively. V C 2015 AIP Publishing LLC. [http://dx.