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In the part of the helix TWTs' nonlinear beam-wave interaction, we developed a 3D relativistic beam-wave interaction model, which can describe the interaction process between the symmetric TMO1 mode RF electromagnetic fields and the relativistic electron beam. This model can describe the 3D RF electromagnetic fields, the 3D motion of the macro-particles, and the 2D space-charge fields. Applying the Lorentz reciprocity theorem, the excited equation is obtained by the theory of waveguide excited. By Lorentz force equation and the conservation of energy, the 3D momentums and positions are obtained. The axial and radial ac space-charge fields are calculated by the harmonics wave means.