From statistical learning theory, the generalization capability of a model is the ability to generalize well on unseen test data which follow the same distribution as the training data. This paper investigates how generalization capability can also improve robustness when testing and training data are from different distributions in the context of speech recognition. Two discriminative training (DT) methods are used to train the hidden Markov model (HMM) for better generalization capability, namely the minimum classification error (MCE) and the soft-margin estimation (SME) methods. Results on Aurora-2 task show that both SME and MCE are effective in improving one of the measures of acoustic model’s generalization capability, i.e. the margin of the model, with SME be moderately more effective. In addition, the better generalization capability translates into better robustness of speech recognition performance, even when there is significant mismatch between the training and testing data. We also applied the mean and variance normalization (MVN) to preprocess the data to reduce the training-testing mismatch. After MVN, MCE and SME perform even better as the generalization capability now is more closely related to robustness. The best performance on Aurora-2 is obtained from SME and about 28% relative error rate reduction is achieved over the MVN baseline system. Finally, we also use SME to demonstrate the potential of better generalization capability in improving robustness in more realistic noisy task using the Aurora-3 task, and significant improvements are obtained.