Unsupervised domain adaptation has achieved significant results by leveraging knowledge from a source domain to learn a related but unlabeled target domain. Previous methods are insufficient to model domain discrepancy and class discrepancy, which may lead to misalignment and poor adaptation performance. To address this problem, in this paper, we propose a unified framework, called distance-aware domain adaptation, which is fully aware of both cross-domain distance and class-discriminative distance. In addition, second-order statistics distance and manifold alignment are also exploited to extract more information from data. In this manner, the generalization error of the target domain in classification problems can be reduced substantially. To validate the proposed method, we conducted experiments on five public datasets and an ablation study. The results demonstrate the good performance of our proposed method.