Remote sensing image scene classification aims to automatically assign semantic labels for remote sensing images. Recently, to overcome the distribution discrepancy of training data and test data, domain adaptation has been applied to remote sensing image scene classification. Most domain adaptation approaches usually explore transferability under the assumption that the source domain and target domain have common classes. However, in real applications, new categories may appear in the target domain. Besides, only considering the transferability will degrade the classification performance due to the strong interclass similarity of remote sensing images. In this article, we present an open set domain adaptation algorithm via exploring transferability and discriminability (OSDA-ETD) for remote sensing image scene classification. To be specific, we propose the transferability technology, which aims at the high interdomain variations and high intraclass diversity of remote sensing images. The purpose of transferability is to reduce the global distribution difference of domains and the local distribution discrepancy of the same classes in different domains. For high interclass similarity in remote sensing images, we adopt the discriminability strategy. The discriminability intends to enlarge the distribution discrepancy of different classes in different domains. To further promote the effectiveness of scene classification, we integrate the transferability and the discriminability into a framework. Moreover, we prove that the algorithm has a unique optimizer.