A novel mm-wave high power microwave device, the ridge-loaded folded waveguide traveling wave tube (TWT), is presented and its linear gain properties are investigated. The perturbed dispersion equation is derived and the small signal growth rate is calculated for different dimensions of ridge and parameters of electron beam. For a cold beam, the linear theory predicts a gain of 1.15 dB/period and a 3-dB small-signal gain bandwidth of 18.51% in Kα-band. The investigation reveals that, with the same beam parameters, the novel slow-wave structure (SWS) has advantage over the folded waveguide SWS in its gain and efficiency. The dimensions of ridge and the beam current may be increased in order to raise the gain.