Convolutional Neural Networks (CNNs) are known to rely more on local texture rather than global shape when making decisions. Recent work also indicates a close relationship between CNN's texture-bias and its robustness against distribution shift, adversarial perturbation, random corruption, etc. In this work, we attempt at improving various kinds of robustness universally by alleviating CNN's texture bias. Specifically, with inspiration from human visual system, we propose a light-weight model-agnostic method, namely Informative Dropout (InfoDrop), to improve interpretability and reduce texture bias. Through extensive experiments, we observe enhanced robustness in various tasks (domain generalization, few-shot classification, robustness against random corruptions and adversarial robustness). Moreover, we show that as a local algorithm, InfoDrop can further improve performance when incorporated with other algorithms for global structure modeling (e.g. Non-Local blocks). To the best of our knowledge, this work is the first attempt to improve different kinds of robustness in a unified model, shedding new light on relationship between shape-bias and robustness, also on new approaches to trustworthy machine learning algorithms.