Single domain generalization (SDG) is a challenging scenario of domain generalization, where only one source domain is available to train the model. Typical SDG methods are based on the adversarial data augmentation strategy, which complements the diversity of source domain to learn a robust model. Existing SDG methods require the source and target domains to have the same label space. However, as target domains may contain novel categories unseen in source label space, this assumption is not practical in many real-world applications. In this paper, we propose a challenging and untouched problem: \textit{Open-Set Single Domain Generalization} (OS-SDG), where target domains include unseen categories out of source label space. The goal of OS-SDG is to learn a model, with only one source domain, to classify a target sample with correct class if it belongs to source label space, or assign it to unknown classes. We design a \textit{CrossMatch} approach to improve the performance of SDG methods on identifying unknown classes by leveraging a multi-binary classifier. CrossMatch generates auxiliary samples out of source label space by using an adversarial data augmentation strategy. We also adopt a consistency regularization on generated auxiliary samples between multi-binary classifiers and the model trained by SDG methods, to improve the model’s capability on unknown class identification. Experimental results on benchmark datasets prove the effectiveness of CrossMatch on enhancing the performance of SDG methods in the OS-SDG setting.