In this paper, a new neural network training algorithm will be devised for function approximator with good generalization characteristics and tested with the time series prediction problem using santaFe competition data sets. To enhance the generalization ability a constraint term of hidden neuraon activations is added to the conventional output error, which gives the curvature smoothing characteristics to multi-layer neural networks. A hybrid learning algorithm of the error-back propagation and Hebbian learning algorithm with weight decay constraint will be naturally developed by the steepest decent algorithm minimizing the proposed cost function without much increase of computational requriements.