A 1D frequency-domain nonlinear model for illustrating the beam-wave interactions of sine waveguide (SWG) traveling-wave tubes (TWTs) was studied. Our model considered space-charge fields and Ohmic losses to make the model closer to practical situations. The sheet beam was split into a series of rectangular electron plates in the axial direction, and the space-charge field was calculated by solving Green's function. The dynamic equations and relativistic equations of motion were solved self-consistently to obtain the nonlinear characteristics of the power saturation, as well as the electron velocity, phase space distributions, etc. A 0.22 THz SWG TWT was used to illustrate and verify the validity of the theoretical model. The output power and gain results were in good agreement with those from the Computer Simulation Technology (CST) 3D particle-in-cell simulation. In addition, the code developed based upon the theoretical model produced faster results than the CST simulation.