With the rapid growth of the e-commerce business scale, to meet customers' demand for efficient order processing, it is of great significance to establish an order management mechanism capable of responding quickly by accurately predicting product demand. This study used real e-commerce order demand data and established a nonlinear autoregressive neural network (NAR) model after pre-processing methods including down-sampling and data set partition to effectively forecast the demand of products in the next 13 weeks. Compared with the Prophet time series prediction framework, NAR had better generalization ability, and the prediction time was reduced by 18.54%. Finally, we summarized two methods' characteristics and gave instructions on applying our model in the real scene. After being deployed in the actual demand management, the trained artificial neural network provides a scientific reference for the data-driven e-commerce decision-making process and brings new advantages over other companies, achieving the rational allocation of resources.