The purpose is to study the handling stability and energy saving mode of energy saving electric vehicles. First, the differences between electric vehicles and traditional fuel vehicles are analyzed. Moreover, based on active safety technology, the control stability, handling stability and driving safety of electric vehicles are improved. Then, based on the vehicle dynamics theory and the proposed assumptions, the modular electric vehicle dynamics model is established, including the wheel model, tire model and driver model, which can effectively control the error of the vehicle model and reduce the difficulty and complexity of vehicle modeling. Next, based on the model predictive control theory, the vehicle steady-state control strategy is established, which can predict and control the state of the electric vehicle in the compound condition and improve the control stability of the vehicle. Finally, the vehicle dynamic model and steady-state control system are simulated and tested. The experimental results show that the simulation results of the established dynamic model of the electric vehicle in angle step condition and single line shifting condition are consistent with the results of professional software, which shows that the established dynamic model can accurately describe the dynamic state of electric vehicle and provides the basis for the research of vehicle stability control strategy. Experimental results of the control strategy under the condition of double line shifting show that the designed control strategy can accurately track the state of the system and constrain the deviation in a small range, so as to ensure the driving stability of the electric vehicle. This exploration provides a reference for the study of dynamic analysis and handling stability control strategy of electric vehicles.