The task of domain generalization is to learn a classification model from multiple source domains and generalize it to unknown target domains. The key to domain generalization is learning discriminative domain-invariant features. Invariant representations are achieved using adversarial domain generalization as one of the primary techniques. For example, generative adversarial networks have been widely used, but suffer from the problem of low intra-class diversity, which can lead to poor generalization ability. To address this issue, we propose a new method called auxiliary classifier in adversarial domain generalization (CloCls). CloCls improve the diversity of the source domain by introducing auxiliary classifier. Combining typical task-related losses, e.g., cross-entropy loss for classification and adversarial loss for domain discrimination, our overall goal is to guarantee the learning of condition-invariant features for all source domains while increasing the diversity of source domains. Further, inspired by smoothing optima have improved generalization for supervised learning tasks like classification. We leverage that converging to a smooth minima with respect task loss stabilizes the adversarial training leading to better performance on unseen target domain which can effectively enhances the performance of domain adversarial methods. We have conducted extensive image classification experiments on benchmark datasets in domain generalization, and our model exhibits sufficient generalization ability and outperforms state-of-the-art DG methods.