The generalization capability of machine learning models, which refers to generalizing the knowledge for an "unseen" domain via learning from one or multiple seen domain(s), is of great importance to develop and deploy machine learning applications in the real-world conditions. Domain Generalization (DG) techniques aim to enhance such generalization capability of machine learning models, where the learnt feature representation and the classifier are two crucial factors to improve generalization and make decisions. In this paper, we propose Discriminative Adversarial Domain Generalization (DADG) with meta-learning-based cross-domain validation. Our proposed framework contains two main components that work synergistically to build a domain-generalized DNN model: (i) discriminative adversarial learning, which proactively learns a generalized feature representation on multiple "seen" domains, and (ii) meta-learning based cross-domain validation, which simulates train/test domain shift via applying meta-learning techniques in the training process. In the experimental evaluation, a comprehensive comparison has been made among our proposed approach and other existing approaches on three benchmark datasets. The results shown that DADG consistently outperforms a strong baseline DeepAll, and outperforms the other existing DG algorithms in most of the evaluation cases.