Rockburst has a large impact on the safe mining of underground mines, and accurate and reliable prediction of rockburst is of great significance to safe production. In order to accurately and effectively predict rockburst, firstly, the stress coefficient, brittleness coefficient, elastic energy index, and integrity coefficient are selected as prediction indicators, and the rockburst prediction index system is established. Secondly, based on the hierarchical analysis method (AHP), improved CRITIC method, and the distance function discriminant method for determining the integrated constant weight, the constant weight is dynamically corrected using the variable weight theory. Then, the effectiveness is introduced to modify the principle of maximum posterior probability, and a Bayesian rockburst intensity grade prediction model with variable weight is constructed. Finally, 15 groups of rockburst engineering examples are selected to verify the reliability and compare the accuracy of the model, and the model is used to predict the rockburst in the middle section of the 1000 m level of Jinchuan No. 2 Mine. The research results show that the accuracy of the Bayesian rockburst prediction model with variable weight can reach 93%. The rockburst intensity grade in the middle section of the 1000 m level of Jinchuan No. 2 Mine is none to slight, and the harm of rockburst is relatively small. The prediction results are in line with the actual situation, which can provide a basis for rockburst prevention and control.