The Kernel Support Vector Machine (Kernel SVM) is one of the machine learning algorithms renowned for its excellent classification performance and high reliability. It is capable of solving highly nonlinear classification problems and has been widely applied in the field of target recognition. The Kernel SVM algorithm is an extension of the SVM, where the original data is mapped to a high-dimensional space via a mapping function for computation. The model determines classification results by solving the optimal classification boundary in the high-dimensional space. However, the results can’t provide classification confidence, leading to poor interpretability and limitations in integrating classification outcomes with other algorithms. To address the issue, a probability distribution assumption for the original model parameters is proposed and a solution is derived, resulting in a Bayesian Kernel SVM model under a probabilistic framework. The applicability and generalization capability of the model are improved by the enhancement.