Fission product yields are key infrastructure data for nuclear applications in many aspects. It is a challenge both experimentally and theoretically to obtain accurate and complete energy-dependent fission yields. We apply the Bayesian neural network (BNN) approach to learn existing fission yields and predict unknowns with uncertainty quantification. We demonstrated that the BNN is particularly useful for evaluations of fission yields when incomplete experimental data are available. The BNN evaluation results are quite satisfactory on distribution positions and energy dependencies of fission yields.