Fast charging station brings new challenges to the utility grid, due to its high peak power and high power fluctuations. The introduction of energy storage system in the electric vehicle charging station can alleviate negative impacts of station operation on the utility grid and reduce the distribution transformer capacity, which brings obvious economic benefit. However, due to the uncertain factors, such as the randomness of fluctuations, the capacity configuration of energy storage systems is necessary. To solve this problem, this paper proposes a capacity configuration optimization approach for the energy storage system in the charging station considering load uncertainty. Taking into account the investment and expanding capacity reconstruction cost and the annual electricity cost, the cost model of the energy storage system with the variable life of the battery is established and solved by robust optimization. Compared with the optimized configuration strategy based on the definite load curve, the proposed configuration strategy based on load uncertainty has shown satisfactory stability and robust performance.