The dispersion relation of a rectangularly periodic cylindrical slow-wave structure (SWS) with an annular electron beam of energy < 100 keV and current around 200 A has been derived and solved numerically. This type of system is typically used in backward wave high-power microwave devices and linear accelerators. The dispersion relation is analysed for both the cold structure (for zero beam current) and structure with an annular beam. The cold structure dispersion relation is characterised by the real value of frequency and wavenumber. When an electron beam propagates through the structure and the beam energy and current are sufficient to produce instability, microwave radiation results. The strength of this radiation can be qualitatively approximated from the temporal growth rate of the instability, which is defined by the imaginary values of the frequency corresponding to the complex conjugate roots of the dispersion relation. The temporal growth rate for various beam parameters has been calculated. The proposed SWS is very easy to be fabricated and can be used in the real experiments for generating high-power microwaves.