In view of the time-varying meshing characteristics of the pressure angle of the concave-convex contact S-gear, a dynamic analysis model of S-gear planetary transmission that accounts for the time-varying pressure angle is proposed. Based on the equation of the line-of-action (LOA) for the S-gear, we derive the calculation formula for the pressure angle and analyze its variation. The time-varying pressure angle is included in the internal excitation of the system and introduced into the nonlinear dynamic model of the system after Fourier function fitting. The dynamic responses of the planetary transmission system are subsequently computed using the Runge-Kutta method. By comparing the dynamic meshing force and dynamic transfer error of the S-gear planetary transmission gear pairs, the influence of the time-varying pressure angle excitation on the system’s dynamic characteristics is analyzed. The results clearly indicate that the time-varying pressure angle has a significant impact on the dynamic response of the planetary gear train, which cannot be ignored. The research results provide a useful source of reference for the dynamic design and vibration control of non-involute planetary gear systems.