A novel slow-wave structure (SWS) called ridge-loaded folded rectangular groove waveguide has been proposed for developing the wideband high-power terahertz (THz) traveling-wave tube (TWT). A new kind of attenuator suitable for this kind of SWS has also been proposed, which can successfully suppress the self-excited oscillations and keep the harmonics to a very low level. An input and output waveguide transition structure which is appropriate for this new kind of SWS is put forward. It can be found from the simulation results that the ridge-loaded SWS can enhance the electric field intensity in the electron beam tunnel so that the average interaction impedance of this ridge-loaded folded rectangular groove waveguide SWS at 0.34 THz is 30.1% higher than that of the folded rectangular groove waveguide SWS. Moreover, the particle-in-cell simulation results reveal that with the sheet electron beam parameters of 27 kV and the 250 mA, the average output power, the gain, and the electronic efficiency of the ridge-loaded folded rectangular groove waveguide TWT at the frequency of 0.34 THz can reach 39 W, 26.99 dB, and 0.59%, respectively. Therefore, the ridge-loaded folded rectangular groove waveguide SWS should be considered as a promising slow-wave circuit for high-power wideband THz radiation source.