Unsupervised domain adaptation (UDA) adopts source domain with large amounts of labeled data to help the learning of the target domain without any label information. In UDA, the source and target domains usually have different data distribution, but share the same label space. But in real open scenarios, label spaces between domains can also be different. In extreme cases, there is no shared class between domains, i.e., all classes in target domain are new classes. In this case, directly transferring the discriminant knowledge in source domain would harm the performance of target domain, lead to negative transfer. As a result, this study proposes an unsupervised new-set domain adaptation with self-supervised knowledge (SUNDA). Firstly, self-supervised learning is adopted to learn the initial features on source and target domains, with the first few layers frozen, in order to keep the target information. Then, the class contrastive knowledge from the source domain is transferred, to help learning discriminant features for target domain. Moreover, the graph-based self-supervised classification loss is adopted to handle the classification problem in target domain without common labels. Experiments are conducted over both digit and face recognition tasks without shared classes, and the empirical results show the competitive of SUNDA compared with UDA and unsupervised clustering methods, as well as new category discovery method.