In this paper a dielectric-loaded folded waveguide slow-wave circuit is presented. The "hot" dispersion relation for slow wave interaction between the traveling wave and linear beam is derived from the fluid dynamical treatment. In the special case where εr=1, the dispersion relation can be simplified with a closed form of the conventional Pierce’s small-signal equation, which confirms the validity of the derivations. By giving the specific parameters, the effects of dielectric loading on the small-signal gain have been studied. The results indicated that in the case of "weak loading" (where d/a<0.1), the gain is flattened and there is no need to readjust the structure parameters beyond a slight adjustment of beam parameters. By considering that the "weak loading" can reduce the ohmic loss of the conductor, this study will be also a guide to the research of the THz folded waveguide traveling-wave tube.