A general equivalent model for slow-wave structure is established in this paper, if the unit cell of the periodic slow-wave structures is represented by a three-port network and the parameters of the equivalent model are determined by a high frequency structural simulator. In this method, there is no need to find a complicated equivalent circuit, and the fields in the tunnels can be calculated by the high frequency software directly. Therefore, the three-port network model is simpler than the analytic method and no more complex than the common equivalent circuit model. A one-dimensional nonlinear beam-wave interaction theory suitable for the folded-waveguide traveling wave tubes (TWTs) is accomplished based on the three-port network model. And a one-dimensional nonlinear beam-wave interaction code, which complies with the MATLAB language, is used to simulate a folded-waveguide TWT. The difference between the results obtained from the code and the experimental data is less than 10%. This theory can be used in the design of novel folded-waveguide TWTs and research on nonlinear simulations.