As one of the typical propulsion systems of the new-energy vehicles (NEVs), the dual-motor driving system (DMDS) is installed and fixed on the bodywork and moves together with the bodywork in space, that is, the DMDS works in non-inertial systems. The previous researches on the DMDS are based on the assumption that the bodywork is stationary. In fact, since the DMDS moves with the bodywork, besides its own excitation forces, it is inevitably affected by the additional inertial terms (AITs) caused by the change in the operating state of the NEVs. In order to investigate the dynamic response and synchronizing characteristic of the DMDS under different motion forms of NEVs, the dynamic model of the DMDS in a non-inertial system is established, considering the permanent magnet synchronous motors (PMSMs), time-varying meshing stiffness and transmission error of gears. Subsequently, the expressions of the AITs are deduced under different non-inertial conditions. The translational motion and circular motion of the vehicle are selected to analyze the dynamic response and synchronizing characteristics of the DMDS in a non-inertial system. The results show that the acceleration has a significant influence on the displacement response of gears, torque and speed of PMSMs, but the torque synchronization and speed synchronization between PMSMs are minimally influenced by both the acceleration and the AITs. Meanwhile, the AITs that affect the displacement response are analyzed and quantified.