In this paper, a new transmission form of a planetary gear transmission coupled with a torsional vibration damper (PGT-D) is proposed where the torsional vibration damper is used to replace the conventional manner a certain member in planetary gear fixed with a box. The advantages of the PGT-D are investigated under complex conditions including start-up, load saltation, and load fluctuations. A dynamic model of the motor and PGT-D connection was established. The dynamic model combines a dynamic asynchronous motor model and a PGT-D model for a variable speed process, wherein the motor electromagnetic characteristics, PGT-D torsional deformation, and time-varying meshing stiffness under variable speed conditions are considered. Then, the simulation results are compared to those of a traditional motor and planetary gear transmission. The torsional vibration damper can reduce resonance points of the system in the common speed range. The PGT-D can effectively reduce the fluctuation level of motor speed and output acceleration, so that the speed of the system can rise smoothly while reducing the amplitude of torque fluctuation on the shaft during the start-up process. Moreover, the influence of time-varying stiffness on the system is analyzed during the load saltation process. Furthermore, the PGT-D can reduce the interference of the fluctuating load on the motor and gear parts.