In order to combine chaos theory and machine learning technology to predict sports performance, a research on sports performance prediction based on chaos theory and machine learning is proposed. This paper takes the sports performance as the goal to predict the data; introduce the chaos theory algorithm, and combine the neural network system and particle swarm optimization algorithm to actively train sports results and ensure the quality of performance prediction. The comparison between shot put data prediction and real data shows that the prediction results given by the model have little deviation and can provide technical services for performance prediction for special sports training. When predicting the sports performance of college students, the prediction accuracy of sports performance of each subject is no less than 90%, which proves that this system can be used in college sports management. The delay time of the model data is short, which is mainly related to the correlation coefficient. When the coefficient is determined to be 0.02, the prediction delay time is 5 s, which can effectively complete the prediction and analysis of sports performance. The combined model has various technical advantages such as chaos theory, neural system, and particle optimization. It has strong sports performance prediction ability and can provide technical support for performance prediction for athletes’ training, college sports management, and other related sports industries.