The increasing ownership of electric vehicles (EVs) has led to the widespread deployment of electric vehicles charging stations (EVCS). However, the high randomness of EV charging behavior pose significant challenges to the load stability of distribution network. To alleviate the deterioration of distribution network stability caused by EV charging load, this paper proposes a multi-objective optimization planning model of EVCS integrated with battery energy storage systems (BESS) based on EV charging demand. The model aims to minimize the overall cost of the EVCS-BESS system, including economic losses due to network losses, user waiting time costs, and system voltage fluctuation, thus optimizing the installation of EVCS in distribution networks to achieve a win-win outcome for EVCS developers, users, and power grid operators. To verify the validity of the proposed planning model, a simulation experiment based on the extended IEEE33 node test system is designed. The experimental results show that using the multi-objective mayfly algorithm (MOMA) for optimization can effectively improve the stability and economic performance of the distribution network.