Based on velocity-modulating model, a nonlinear wave-beam interaction theory for folded-waveguide traveling wave tubes is developed. In this theory, the continuing beam is treated as discrete macro-particles with different initial phases. Then beam-wave interaction and energy exchange are analyzed at each crossing point between beam-tunnel and wave-tunnel. Compared with PIC result, the error of output power predicted by this model is within 10%, and the error of saturated length is within 15%. The results of this model are significant for designing folded-waveguide traveling wave tubes.