The accuracy of deep learning (e.g., convolutional neural networks) for an image classification task critically relies on the amount of labeled training data. Aiming to solve an image classification task on a new domain that lacks labeled data but gains access to cheaply available unlabeled data, unsupervised domain adaptation is a promising technique to boost the performance without incurring extra labeling cost, by assuming images from different domains share some invariant characteristics. In this paper, we propose a new unsupervised domain adaptation method named Domain-Adversarial Residual-Transfer (DART) learning of Deep Neural Networks to tackle cross-domain image classification tasks. In contrast to the existing unsupervised domain adaption approaches, the proposed DART not only learns domain-invariant features via adversarial training, but also achieves robust domain-adaptive classification via a residual-transfer strategy, all in an end-to-end training framework. We evaluate the performance of the proposed method for cross-domain image classification tasks on several well-known benchmark data sets, in which our method clearly outperforms the state-of-the-art approaches.