Abstract: In this paper, an approach to the discriminative training of hidden Markov model (HMM) is presented. The forward probability calculation of HMM is accomplished within the framework of a multilayer feedforward neural network. Based on this framework, by making use of the back-propagation method of computing partial derivatives, the maximization of mutual information can be achieved through the gradient ascent optimization process, and thus the discriminative training of HMM is performed. This approach to the training of HMM is called back-propagation training approach. Additionally, a more numerically robust algorithm is also designed for implementing this approach. The superiority of this approach is proved by the results of the speech recognition experiments.