How to accurately forecast seasonal time series is very important for many business area such as marketing decision, planning production and profit estimation. In this paper, we propose a weighted gradient Radial Basis Function Network based AutoRegressive (WGRBF-AR) model for modeling and predicting the nonlinear and non-stationary seasonal time series. This WGRBF-AR model is a synthesis of the weighted gradient RBF network and the functional-coefficient autoregressive (FAR) model through using the WGRBF networks to approximate varying coefficients of FAR model. It not only takes the advantages of the FAR model in nonlinear dynamics description but also inherits the capability of the WGRBF network to deal with non-stationarity. We test our model using ten-years retail sales data on five different commodity in US. The results demonstrate that the proposed WGRBF-AR model can achieve competitive prediction accuracy compared with the state-of-the-art.