提出了多层前向神经网络的新型二阶递推学习算法 .该算法不仅能使网络各层误差而且使二阶导数信息因子反向传播 .证明了新算法等价于Newton迭代法并且有二阶收敛速度 .它实现了Newton搜索方向和Hessian阵逆的递推运算 ,其计算量几乎与普通递推最小二乘法相当 .由算法性能分析证明新算法优于Karayiannis等人的二阶学习算法 . A new type of second order recursive learning algorithm for multi-layer forward neural networks is proposed, which can not only make the network layers error but also backpropagate the second-order derivative information factor. It is proved that the new algorithm is equivalent to the Newton iterative method and has two Order convergent speed, which achieves the recursive computation of Newton search direction and Hessian matrix inverse, which is almost the same as that of ordinary recursive least square method.The algorithm performance analysis proves that the new algorithm is superior to the second-order learning algorithm of Karayiannis et al.