As international trade has been developing at an unprecedented rate, export product competitiveness is significant in a country's trade system. At present, neural network algorithms are extensively used in economic forecasting. Scholars have verified the effectiveness of neural networks, especially long short term memory (LSTM) model, compared with other nonlinear prediction methods. However, there are still research blanks in forecasting economic indicators related to export product competitiveness, and there is little research on the improved LSTM model combined with other algorithms. To address this limitation, this article established a quantitative index system for export product competitiveness composed of four highly recognized indicators such as revealed comparative advantage index, net export revealed comparative advantage index, international market share index, and economic value added. After collecting the relevant economic data, the single LSTM model was used to predict the future trend of China's machinery and equipment export product competitiveness. Based on the shortcomings exposed in applying single LSTM prediction, the article innovatively designs a combined forecast model of LSTM and seasonal autoregressive integrated moving average, and whose effectiveness and superiority are proved by the mean square error value. Finally, the article points out that this model plays an important role in national trade policy making. It is optimistic about the development of deep learning in international trade product competitiveness indicators prediction.