The kernel support vector machine (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 support vector machine, 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 cannot provide classification confidence, leading to poor interpretability and limitations in integrating classification outcomes with other algorithms. To address this issue, this paper proposes a probability distribution assumption for the original model parameters and derives a solution, resulting in a Bayesian kernel SVM model under a probabilistic framework. This enhancement improves the model's applicability and generalization capability.