Abstract: In this paper, a basis function neural network is constructed, of which the hidden-layor neurons are activated with linear independence basis function.Accordingly, the learning algorithm for the constructed neural network is derived and a fast algorithm based on exponential-growth and binary-delete search strategy is proposed to determinate the optimal number of hidden-layor neurons.The simulation results substantiate that our algorithm can adaptively, quickly and efficiently determine number of hidden neurons in the neural network.