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The progress of construction and safe production in mining, water conservancy, tunnels, and other types of deep underground engineering is seriously affected by rockburst disasters. This makes it essential to accurately predict rockburst intensity. In this paper, the ratio of maximum tangential stress of surrounding rock to rock uniaxial compressive strength (σθ/σc), the ratio of rock uniaxial compressive strength to rock uniaxial tensile strength (σc/σt), and the elastic energy index of rock (Wet) were chosen as input indices, and rockbursts were graded as level I (none rockburst), level II (light rockburst), level III (medium rockburst), and level IV (strong rockburst). A total of 104 groups of rockburst engineering samples, collected widely from around the world, were divided into a training set (84 groups of samples) and a test set (20 groups of samples). Based on the kernel principal component analysis (KPCA), the adaptive particle swarm optimization (APSO) algorithm, and the support vector machine (SVM), the KPCA-APSO-SVM model was established. The proposed model showed satisfactory classification performance: the prediction accuracies of the training set and test set were 98.81% and 95%, respectively. In addition, the trained prediction model was applied to five rockburst engineering cases and compared with the BP neural network model, SVM model, and APSO-SVM model. The comparative results show that the KPCA-APSO-SVM model has a higher prediction accuracy; as such, it provides a new reliable method for rockburst prediction. [ABSTRACT FROM AUTHOR]