In this paper, a recurrent neural network based fuzzy inference system (RNFIS) for prediction is proposed. A recurrent network is embedded in the RNFIS by adding feedback connections in the second layer and in the output layer. In this paper, a hybrid learning algorithm is used to train the RNFIS model. This algorithm uses a modified version of the bees algorithm and gradient descent (GD). In the basic version of bees algorithm, the algorithm performs a kind of neighborhood search combined with random search. To improve the local search ability of the bees algorithm and help the algorithm to jump out from the local optimum, a modification is performed by applying three kinds of crossovers to the elite individuals based on different conditions of current state. To verify the performance of the proposed method, this method is applied to a benchmark time series and a real problem. The performance compared with the basic bees algorithm, gradient descent (GD), differential evolution (DE), ...