Summary: A weights-and-structure-determination (WASD) algorithm is proposed for the neural network using bipolar sigmoid activation functions together with subsequent iterations, which is the combination of the Levenberg-Marquardt algorithm and the weights-direct-determination method for neural network training. The proposed algorithm, combined with the Neural Network Toolbox of MATLAB software, aims at remedying the common weaknesses of traditional artificial neural networks, such as long-time learning expenditure, difficulty in determining the network structure, and to-be-improved performance of learning and generalization. Meanwhile, the WASD algorithm has good flexibility and operability. Taking data fitting of nonlinear functions for example, numerical experiments and comparison results illustrate the superiority of the WASD algorithm for determining the optimal number and optimal weights of hidden neurons. And the resultant neural network has more excellent performance on learning and generalization.