In recent years, cross-border e-commerce has become a new economic growth point for many countries. However, in the purchasing process, most cross-border e-commerce enterprises still use stocking strategies based on general experience. Since goods need to be reordered immediately when they are out of stock, a lack of a scientifically-based purchasing plan may result in excessive inventory and a low inventory turnover rate. Thus, the ability to determine appropriate order quantity under uncertain cross-border market demands is key to improving the inventory control of cross-border e-commerce enterprises. To ensure the quality of cross-border e-commerce products and maximise profits, it is crucial to formulate an effective and practical purchasing strategy. Based on existing research, this paper examines a cross-border e-commerce purchasing strategy under uncertainty by using the newsvendor model and setting expected profit maximisation as the goal. Specifically, this paper explores the optimal purchasing strategy for cross-border e-commerce products under discrete and continuous stochastic demands.