In this thesis, we consider estimation of regression function one or several explanatory variables in which regression function is modeled as a linear combination of a family of basis functions. As regards, radial basis function neural network can be considered as the nonlinear regression model. We apply the model as an estimation to the function of linear regression. In fact, we construct nonlinear regression using radial basis function network from a finite and noisy data. For this purpose, first radial basis functio is introduced with a hyperparameter. In order to determine the nonlinear function of the model and also estimate the weight parameters,radial basis function network and regularization method are used. Also to estimate unknow parameters of the model generalization information criteria is used.