Multisource unsupervised domain adaptation (MUDA) is an important and challenging topic for target classification with the assistance of labeled data in source domains. When we have several labeled source domains, it is difficult to map all source domains and target domain into a common feature space for classifying the targets well. In this article, a new progressive multisource domain adaptation network (PMSDAN) is proposed to further improve the classification performance. PMSDAN mainly consists of two steps for distribution alignment. First, the multiple source domains are integrated as one auxiliary domain to match the distribution with the target domain. By doing this, we can generally reduce the distribution discrepancy between each source and target domains, as well as the discrepancy between different source domains. It can efficiently explore useful knowledge from the integrated source domain. Second, to mine assistance knowledge from each source domain as much as possible, the distribution of the target domain is separately aligned with that of each source domain. A weighted fusion method is employed to combine the multiple classification results for making the final decision. In the optimization of domain adaption, weighted hybrid maximum mean discrepancy (WHMMD) is proposed, and it considers both the interclass and intraclass discrepancies. The effectiveness of the proposed PMSDAN is demonstrated in the experiments comparing with some state-of-the-art methods.