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Multi‐source domain adaptation (MDA) aims to leverage knowledge from multiple source domains to improve the classification performance on target domains. Different degrees of distribution discrepancies between every two domains pose a huge challenge to MDA tasks. Most works focus on extracting features shared by all domains, which is critical but not enough to reduce distribution discrepancies. In this paper, we propose a method named as common‐specific feature learning (CSFL). Constituting a framework of feature learning, CSFL explores a subspace where the combination of common and specific features makes learned representations comprehensive. Based on this framework, we conduct a metric learning method for learning a discriminative feature representation. Considering redundant information caused by source domains is likely to hurt the performance, we impose an effective low‐rank constraint to remove the redundant information. Further, we adopt structure consistent constraint to preserve the local structure in each domain. CSFL has obtained about 1–5% improvement of mean accuracy, compared to the state‐of‐the‐art shallow methods. Further, compared with 90.2% and 89.4% of the best baseline deep method, CSFL achieves mean accuracy of 90.8% and 89.7% on the Office‐31 and ImageCLEF‐DA datasets respectively. The encouraging results validate the effectiveness of our method. [ABSTRACT FROM AUTHOR]