In this paper, we propose a new supervised learning method for adaptive neuro-fuzzy inference system (ANFIS) training, which uses the expectation maximization (EM) algorithm and extended Kalman smoother (EKS) together; we refer to it here as the EM-EKS training method. While the EKS tunes the ANFIS parameters, the EM algorithm estimates the parameters of the Kalman filter and avoids non-optimal performance. Besides, we also propose a new algorithm to select the initial values of the EKS parameters. We compare the EM-EKS method of ANFIS training with traditional ANFIS training. Although the new training method requires more computing time, it yields improved RMSE values in function approximation and prediction problems. Examples of benchmark function approximation and prediction illustrate the effectiveness of the EM-EKS ANFIS training method.