Stimulated polariton scattering (SPS) is one of the most important non-collinear phase-matching nonlinear process. In SPS, the angle between the THz and pump waves is as large as 65°, so it is necessary to study the spatial intensity distributions of the pump, Stokes and THz waves effected by the non-collinear phase-matching. In this work, we take the injection-seeded terahertz wave parametric generator (is-TPG) as an example to obtain the numerical solutions of the coupled-wave equations. The simulation results are focused on the spatial-temporal intensity distributions and the energy input-output characteristics. It is notable that the spatial intensity distributions of the pump and Stokes beams along the THz-wave propagation direction are not uniform as the inputs. The pump wave is depleted along the THz-wave propagation direction while the Stokes wave is increasing at the same time.