A new learning algorithm for feedforward neural networks based on the hybrid GNBFGS method is presented. The algorithm combines the better features of both Gauss-Newton and BFGS methods

which make use of the special structure of the problem

and the order of convergence is superlinear even quadratic.It gives faster and more reliable learning property compared with the BP algorithm.By making use of the feature for distinguishing the non-zero-residual and zero-residual problem of hybrid GN-BFGS method

a technique to adjust the number of hidden units in learning process is proposed to ensure learning and generalization capabilities of networks.The results of sample systems show the effectiveness of the algorithm.