Abstract: This paper proposes a new type of folded waveguide slow-wave structure with variable parameters, which can greatly increase the device's saturation gain. Combining small-signal theory analysis and three-dimensional PIC numerical simulation of beam-wave interaction process, the paper also proposes a theoretical design method for this variable-parameter slow-wave structure. A 0.345 THz two-stage folded waveguide slow-wave structure is designed and simulated, which proves that the two-stage slow-wave structure has higher electron conversion efficiency and saturation gain than the conventional uniform slow-wave structure under the same working conditions and can be widely applied to multi-stage structures.