THe purpose of this study is to forecast of runoff hydrographs according to rainfall event in a stream. The neural network theory as a hydrologic blackbox model is used to solve hydrological problems. The Back-Propagation(BP) algorithm by the Levenberg-Marquardt(LM) techniques and Radial Basis Function(RBF) network in Neural Network(NN) models are used. Runoff hydrograph is forecasted in Bocheongstream basin which is a IHP the representative basin. The possibility of a simulation for runoff hydrographs about unlearned stations is considered. The results show that NN models are performed to effective learning for rainfall-runoff process of hydrologic system which involves a complexity and nonliner relationships. The RBF networks consist of 2 learning steps. The first step is an unsupervised learning in hidden layer and the next step is a supervised learning in output layer. Therefore, the RBF networks could provide rather time saved in the learning step than the BP algorithm. The peak discharge both BP algorithm and RBF network model in the estimation of an unlearned are a is trended to observed values.