In this paper, the Bayesian recurrent neural network is proposed to predict time series data. A neural network predictor requests proper learning strategy to adjust the network weights, and one needs to prepare for non-linear and non-stationary evolution of network weights. The Bayesian neural network in this paper estimates not the single set of weights but the probability distributions of weights. In other words, the weights vector is set as a state vector of state space method, and its probability distributions are estimated in accordance with the particle filtering process. This approach makes it possible to obtain more exact estimation of the weights. In the aspect of network architecture, it is known that the recurrent feedback structure is superior to the feedforward structure for the problem of time series prediction. Therefore, the recurrent neural network with Bayesian inference, what we call Bayesian recurrent neural network (BRNN), is expected to show higher performance than the normal neural network. To verify the proposed method, the time series data are numerically generated and various kinds of neural network predictor are applied on it in order to be compared. As a result, feedback structure and Bayesian learning are better than feedforward structure and backpropagation learning, respectively. Consequently, it is verified that the Bayesian reccurent neural network shows better a prediction result than the common Bayesian neural network.