Unsupervised domain adaptation has been proved to be a promising approach to solve the problem of dataset bias. To employ source labels in the target domain, it is required to align the joint distributions of source and target data. To do this, the key research problem is to align conditional distributions across domains without target labels. In this paper, we propose a new criterion of domain-shared group-sparsity that is an equivalent condition for conditional distribution alignment. To solve the problem in joint distribution alignment, a domain-shared group-sparse dictionary learning method is developed towards joint alignment of conditional and marginal distributions. A classifier for target domain is trained using the domain-shared group-sparse coefficients and the target-specific information from the target data. Experimental results on cross-domain face and object recognition show that the proposed method outperforms eight state-of-the-art unsupervised domain adaptation algorithms.