Charging station batteries which are widely used in stand-alone solar system for charging electric vehicles (EVs) are easily damaged by overcharging or by deep discharging. The design of a control system however requires a good understanding of the dynamic behaviour of such batteries and mainly the voltage issue. In this paper, we mainly focused on lead-acid battery as one of the powerful charging batteries. A mathematical model of this type of batteries is investigated. The expression of voltage discharging is given according to discharging time of the battery, discharging current, and other electrical parameters. The parameters of the model are extracted from battery datasheets and using some fitting techniques. The same model of the battery terminal voltage is also used to describe charging processes battery. For this case only the parameters of the battery model are changed. The proposed model is simulated with Matlab/Simulink and the obtained results are compared with experimental results recorded from charging and discharging process using a SW280-YUASA battery. The obtained results and performed comparison show the effectiveness of the proposed model.