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This paper studies a new, practical but challenging problem, called Class-Incremental Unsupervised Domain Adaptation (CI-UDA), where the labeled source domain contains all classes, but the classes in the unlabeled target domain increase sequentially. This problem is challenging due to two difficulties. First, source and target label sets are inconsistent at each time step, which makes it difficult to conduct accurate domain alignment. Second, previous target classes are unavailable in the current step, resulting in the forgetting of previous knowledge. To address this problem, we propose a novel Prototype-guided Continual Adaptation (ProCA) method, consisting of two solution strategies. 1) Label prototype identification: we identify target label prototypes by detecting shared classes with cumulative prediction probabilities of target samples. 2) Prototype-based alignment and replay: based on the identified label prototypes, we align both domains and enforce the model to retain previous knowledge. With these two strategies, ProCA is able to adapt the source model to a class-incremental unlabeled target domain effectively. Extensive experiments demonstrate the effectiveness and superiority of ProCA in resolving CI-UDA. The source code is available at https://github.com/Hongbin98/ProCA.git