In recent years, many deep learning-based methods have been used in the field of fault diagnosis and have achieved good results. However, it is difficult to obtain generator fault sample data. In a case of a small amount of data, deep learning-based methods have over-fitting phenomenon, resulting in poor model generalization ability and low diagnostic accuracy. In order to solve this problem, this paper proposes a fault diagnosis method based on the random variational inference Bayesian neural network. This method is based on Bayesian inference and random variational inference, which can obtain a more reliable model based on a small amount of data. Obtaining the probability distribution of the parameters of each layer of the network can effectively solve the problem of overfitting. The evidence lower bound derived function TraceGraph ELBO is used to carry out random variational inference, which solves the problem of low diagnostic accuracy of the derived function Trace ELBO. This method is applied to the fault diagnosis of generator bearings and compared with other methods. The results show that the proposed method has higher diagnostic performance when the amount of fault sample data is small.