A previously developed field matching technique for the analysis of a metal disc-loaded circular waveguide, excited in a non-azimuthally varying transverse electric (TE) mode, was used to explore the advantage of the presence of a dielectric in controlling its dispersion characteristics for widening the bandwidth of a gyro-travelling-wave tube (gyro-TWT). The modelled structure, consisting of an axial dielectric insert and dielectric discs alternately placed between metal discs, was analysed considering the propagating and stationary waves in the disc-free and disc-occupied regions, respectively. While the axial dielectric insert gave no specific advantage with respect to dispersion control, the dielectric disc axial thickness, permittivity and periodicity and disc-hole radius quite effectively shaped the structure dispersion. In controlling the structure dispersion, the disc-hole radius, which was not as effective as the disc-periodicity in a conventional metal disc-loaded waveguide, became more effective, though the disc periodicity did not enjoy any additional advantage. The thickness or permittivity of dielectric discs controlled the passband frequencies and hence helped attain operating frequencies of a gyro-TWT. The passband of the lower and higher order modes remaining unchanged by a suitable choice of the structure parameters, a higher order mode, for instance the TE02 mode, gave a better wideband potential than the TE01 mode.