The dispersion characteristics of radial-line slow wave structures with shallow rectangular grooves are examined using the Borgins's potential function method. The whole structure is considered as one region with grooves that satisfy the Rayleigh criterion. In this region, an appropriate Fourier expansion of traveling waves is applicable. By applying suitable boundary conditions, the dispersion equations of an infinite system are obtained, which are solved numerically by calculation and simulation. Comparisons of analytic and numerical results with calculation and simulation show excellent agreement and justify a high degree of confidence in the validity of the theory. The Q-factor and coupling impedance of TM02 mode are higher than that of TM01 mode and that of the quasi-TEM mode with special parameters, while the starting current of TM02 mode is lower than that of TM01 and quasi-TEM modes, which makes the TM02 mode dominate over the start-up of the oscillation. Structural parameters, including period length, corrugation depth, and tube width as well as original radius are considered in detail to choose the exact operating frequency and modes of V-band radial-line backward-wave oscillators (BWOs). More importantly, the presented new dispersion equations can provide a theoretical guidance for the design of V-band radial-line BWOs.