The developing process of steering system has experienced four phases from the simple mechanical steering system (MS), hydraulic steering system (HPS) to electric-hydraulic steering system (EHPS), till the electric power steering system (EPS) with lower energy consumption and higher performance. EPS has been found of more and more applications in the rapid development of new energy electric vehicles. This paper aims at the dynamic research of the control strategy of EPS system. Through analyzing the simplified structure model of EPS system, the mathematical models of steering wheel-steering shaft, ECU-Assist motor and rack-pinion are established by Newton's second law. The design of curve-line assist curve is one of the main research points, especially the determination method for the function expression of all the segments in the curve-line assist curve. In order to adapt different operating conditions and reduce the side-effect of non-linear factors, three steering control modes and three compensation control methods are proposed in this paper. For verifying the effect of the control strategy proposed in this paper, the simulation model of the EPS system is built in MATLAB/Simulink®. In the simulation process, it is shown that the control strategy proposed in this paper can bring good maneuverability and stability for the EPS system and the return-to-center control and the damping compensation method can improve the dynamic performances of the EPS system.