Data augmentation is an effective way to improve the generalization capability of modern deep learning models. However, the underlying augmentation methods mostly rely on handcrafted operations. Moreover, an augmentation policy useful to one dataset may not transfer well to other datasets. Therefore, Automated Data Augmentation (AutoDA) methods, like \textit{AutoAugment} and \textit{Population-based Augmentation}, have been proposed recently to automate the process of searching for optimal augmentation policies. However, the augmentation policies found are not adaptive to the dataset used, hindering the effectiveness of these AutoDA methods. In this paper, we propose a novel AutoDA method called \texttt{AdaAug} to efficiently learn adaptive augmentation policies in a class-dependent and potentially instance-dependent manner. Our experiments show that the adaptive augmentation policies learned by our method transfer well to unseen datasets such as the Oxford Flowers, Oxford-IIT Pets, FGVC Aircraft, and Stanford Cars datasets when compared with other AutoDA baselines. In addition, our method also achieves state-of-the-art performance on the CIFAR-10, CIFAR-100, and SVHN datasets.