The learning strategy of the radial basis function network (RBFN) commonly uses a hybrid learning process to identify the structure and then proceed to search the model parameters, which is a time-consuming procedure. We proposed an evolutionary way to automatically configure the structure of RBFN and search the optimal parameters of the network. The strategy can effectively identify an appropriate structure of the network by the orthogonal least squares algorithm and then systematically search the optimal locations of centres and the widths of their corresponding kernel function by the genetic algorithm. The proposed strategy of auto-configuring RBFN is first testified in predicting the future values of the chaotic Mackey-Glass time series. The results demonstrate the superiority, on both effectiveness and efficiency, of the proposed strategy in predicting the chaotic time series. We then further investigate the model's suitability and reliability in flood forecast. The Lan-Young River in north-east Taiwan is used as a case study, where the hourly river flow of 23 flood events caused by typhoons or storms is used to train and validate the neural networks. The back propagation neural network (BPNN) is also performed for the purpose of comparison. The results demonstrate that the proposed RBFN has much better performance than the BPNN. The RBFN not only provides an efficient way to model the rainfall-runoff process but also gives reliable and precise one-hour and two-hour ahead flood forecasts.