Gradual Domain Adaptation (GDA), in which the learner is provided with additional intermediate domains, has been theoretically and empirically studied in many contexts. Despite its vital role in security-critical scenarios, the adversarial robustness of the GDA model remains unexplored. In this paper, we adopt the effective gradual self-training method and replace vanilla self-training with adversarial self-training (AST). AST first predicts labels on the unlabeled data and then adversarially trains the model on the pseudo-labeled distribution. Intriguingly, we find that gradual AST improves not only adversarial accuracy but also clean accuracy on the target domain. We reveal that this is because adversarial training (AT) performs better than standard training when the pseudo-labels contain a portion of incorrect labels. Accordingly, we first present the generalization error bounds for gradual AST in a multiclass classification setting. We then use the optimal value of the Subset Sum Problem to bridge the standard error on a real distribution and the adversarial error on a pseudo-labeled distribution. The result indicates that AT may obtain a tighter bound than standard training on data with incorrect pseudo-labels. We further present an example of a conditional Gaussian distribution to provide more insights into why gradual AST can improve the clean accuracy for GDA.