In this article, a relativistic backward wave oscillator (RBWO) with sectional slow wave structures (SWSs) has been designed to generate a long high-power microwave (HPM) pulse at two different frequencies. Two individual SWSs were cascaded using a drift section (drift section-II) that separated them at a sufficient distance to generate dual microwave frequencies. The first section of the SWS (SWS-I) has been designed to generate S-band frequency and the second section of the SWS (SWS-II) to generate C-band frequency. A rectangular resonant reflector (RR) has been used to reflect the backward traveling wave into a forward wave toward the collector. The drift section-II also acted as an RR for the C-band frequency in addition to make the phase adjustment between the backward and forward microwaves and end reflections of SWS-I. The performance of the dual-band RBWO with sectional SWSs has been studied through the particle-in-cell (PIC) simulation by a finite difference time domain (FDTD)-based numerical code. The present simulation predicted a total RF output power of ~600 MW in TM01 mode at ~3.6 and ~4.5 GHz with a power conversion efficiency of ~20% for an annular electron beam with voltage ~550 kV, developed current ~5.4 kA, and the guiding magnetic field of ~1.3 T. A clear and more stable RF output power up to 100 ns of simulation time at both operating frequencies was observed with a frequency difference (between S- and C-band) of ~0.9 GHz.