Multi-source driving transmission systems, in which the gear assembly is driven by multiple induction motors, are extensively used in new energy, aerospace, marine engineering, and in other fields. The multi-source driving system faces an even-load distribution problem, i.e., torque or speed synchronization issues. In this study, the synchronization characteristics of a multi-source driving transmission system under an impact load at different load change rates are studied. An accurate electromechanical coupling dynamic model of the system considering the flexible shafts, support bearing and meshing gear pair is established by applying virtual equivalent shaft elements. By considering the time-varying meshing and the coupling effects of the dynamic electric motor and the speed, torque and stator current synchronization characteristics are investigated using this model. Computational results show that the influence of the load change rate on the speed synchronization characteristics of the system is minor, but has a significant influence on the torque and stator current synchronization characteristics. The stator current root mean square value (RMS) can be chosen as a feedback signal to monitor the synchronization characteristics of the system. The proposed research provides the theoretical basis for the formulation of the synchronization control strategy for multi-source driving transmission systems.