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bp neural network algorithm to solve optimization problems, one of the advanced algorithm, the paper discusses the neural network in the most widely used feed-forward neural network. Its network weights learning algorithm in the greatest impact is the error back-propagation algorithm (back-propagation algorithm referred to as BP). BP algorithm for the existence of local minimum points, such as the shortcomings of slow convergence. Optimization theory based on the Levenberg-Marquardt algorithm ignores the second-order item. In this paper, the discussion when the error is not zero or not that is second-order linear function of S (W) can not be ignored when the Hesse matrix of approximate calculation, and then training the network.