The COVID-19 outbreak continues to spread around the world, with more than 200 countries and regions having confirmed cases, and various responses to the outbreak. In order to predict the development trend of the epidemic in different countries and analyze the effectiveness of relevant prevention and control measures, a BP neural network (BPNN) model was established to predict the development of the epidemic in China, the United States and Italy in the next 180 days based on relevant data of the epidemic. The results show that the BP neural network model can reasonably predict the development of the epidemic. In the three samples, the cumulative number of confirmed cases in China has basically stabilized, and the peak of the epidemic in Italy and the United States will occur no earlier than mid-January next year. The prediction results of this study are basically consistent with the actual epidemic situation and the policies issued by relevant departments, which can provide a scientific basis for effective epidemic prevention and control measures.