In pattern classification, there may not exist labeled patterns in the target domain to train a classifier. Domain adaptation (DA) techniques can transfer the knowledge from the source domain with massive labeled patterns to the target domain for learning a classification model. In practice, some objects in the target domain are easily classified by this classification model, and these objects usually can provide more or less useful information for classifying the other objects in the target domain. So a new method called distribution adaptation based on evidence theory (DAET) is proposed to improve the classification accuracy by combining the complementary information derived from both the source and target domains. In DAET, the objects that are easy to classify are first selected as easy-target objects, and the other objects are regarded as hard-target objects. For each hard-target object, we can obtain one classification result with the assistance of massive labeled patterns in the source domain, and another classification result can be acquired based on the easy-target objects with confidently predicted (pseudo) labels. However, the weights of these classification results may vary because the reliabilities of the used information sources are different. The weights are estimated by mean difference reflecting the information source quality. Then, we discount the classification results with the corresponding weights under the framework of the evidence theory, which is expert at dealing with uncertain information. These discounted classification results are combined by an evidential combination rule for making the final class decision. The effectiveness of DAET for cross-domain pattern classification is evaluated with respect to some advanced DA methods, and the experiment results show DAET can significantly improve the classification accuracy.