Abstract: Nuclear data is the basis for nuclear physics fundamental research, nuclear engineering, and applications in nuclear technology. Neutron-induced nuclear fission reaction cross-sections are a primary component of nuclear data, with significant applications in advanced nuclear energy system development and nuclear astrophysics research. This work, based on Bayesian theory, employs a feedforward neural network with four hidden layers. The Markov Chain Monte Carlo (MCMC) simulation method and Kullback–Leibler divergence (KL) are utilized. A Bayesian neural network computational model is established for neutron-induced fission reaction cross-section data of ²³⁸U, ²³²Th, and ²³⁹Pu, with incident energy and fission cross-section as input and output parameters, respectively. Experimental data and evaluation data of fission cross-sections for ²³⁸U and ²³²Th in the neutron energy range of 1~200 MeV and for ²³⁹Pu in the range of 1~100 MeV are selected for model training. The MCMC method is employed to construct a Markov chain to approximate the target distribution, and the KL divergence constraint method is combined to optimize the loss function. The research results indicate that the Bayesian neural network prediction model can effectively reproduce experimental data from literature, demonstrating strong predictive capabilities. This provides a reference for addressing the significant discrepancies in experimental data for ²³⁸U and ²³²Th with incident neutron energies greater than 200 MeV and for ²³⁹Pu with energies greater than 100 MeV, as well as for nuclear data evaluation.