To optimize the layout of an electric vehicle charging network, and thus improving charging service capacity and efficiency, this paper develops a charging network planning model that considers both captured traffic flows and charging driving distance. The uncertainty of the initial state of charge of the electric vehicle power battery leads to stochastic characteristics of the captured traffic flows of the charging network. The Monte Carlo simulation method is used to analyze its probability characteristics. To improve the charging service capability in any situation, the model takes the maximum value of minimum traffic flows captured by the charging network as one of the optimization objectives. To upgrade charging efficiency, another optimization goal of the model is to minimize the average charging driving distance. In addition, the model considers the opportunity constraints of charging driving distance and the number of charging station construction constraints, and uses a non-dominated sorting genetic algorithm II (NSGA-II) to analyze the proposed model to obtain the Pareto optimal solution set. Finally, a simulation experiment is conducted on a 25-node transportation network to verify the effectiveness of the proposed method. Based on the results, the impact of chance constrained confidence and the number of charging stations on the solutions is analyzed.