Adversarial images are designed to mislead deep neural networks (DNNs), attracting great attention in recent years. Although several defense strategies achieved encouraging robustness against adversarial samples, most of them fail to improve the robustness on common corruptions such as noise, blur, and weather/digital effects (e.g. frost, pixelate). To address this problem, we propose a simple yet effective method, named Progressive Data Augmentation (PDA), which enables general robustness of DNNs by progressively injecting diverse adversarial noises during training. In other words, DNNs trained with PDA are able to obtain more robustness against both adversarial attacks as well as common corruptions than the recent state-of-the-art methods. We also find that PDA is more efficient than prior arts and able to prevent accuracy drop on clean samples without being attacked. Furthermore, we theoretically show that PDA can control the perturbation bound and guarantee better generalization ability than existing work. Extensive experiments on many benchmarks such as CIFAR-10, SVHN, and ImageNet demonstrate that PDA significantly outperforms its counterparts in various experimental setups.