A method using unscented Kalman filter for training radial-basis-function networks (RBFN) is studied. Unscented Kalman filter (UKF) shows great advantages than algorithms such as extended Kalman filter (EKF) and dual extended Kalman filter(DEKF) by extending the nonlinear functions using the second order approximation comparing to the one order in EKF and DEKF. And the most important is that the algorithm doesn't need to calculate the system Jacobbi matrix, so the computational complication can be reduced greatly. Simulation results show the validity of the algorithm in training RBFN for chaotic time series prediction and classification problems.