By using the energy storage buffer system, we can compensate the pulse power of fast charging electric vehicles (EV) and reduce the adverse influence on the distribution network caused by the fast charging stations. This paper studies the topology structure of fast charging station with energy storage buffer system and the fast charging power characteristics of different types of batteries. Then taking the distribution network real power change limit into account, we propose an operation mode of the energy storage buffer system of the fast charging stations and its current control strategy. Furthermore, to design the storage buffer system module and its control parameters, we combine the configuration of fast charging stations to deduce the operation parameters of the storage buffer system. Using Matlab/Simulink software, we build a model of fast charging station with energy storage buffer system, analyze the dynamic characteristics of fast charging station with different pulse charging power, and verify the correctness and effectiveness of the control strategy.