Previous OOD detection systems only focus on the semantic gap between ID and OOD samples. Besides the semantic gap, we are faced with two additional gaps: the domain gap between source and target domains, and the class-imbalance gap between different classes. In fact, similar objects from different domains should belong to the same class. In this paper, we introduce a realistic yet challenging setting: class-imbalanced cross-domain OOD detection (CCOD), which contains a well-labeled (but usually small) source set for training and conducts OOD detection on an unlabeled (but usually larger) target set for testing. We do not assume that the target domain contains only OOD classes or that it is class-balanced: the distribution among classes of the target dataset need not be the same as the source dataset. To tackle this challenging setting with an OOD detection system, we propose a novel uncertainty-aware adaptive semantic alignment (UASA) network based on a prototype-based alignment strategy. Specifically, we first build label-driven prototypes in the source domain and utilize these prototypes for target classification to close the domain gap. Rather than utilizing fixed thresholds for OOD detection, we generate adaptive sample-wise thresholds to handle the semantic gap. Finally, we conduct uncertainty-aware clustering to group semantically similar target samples to relieve the class-imbalance gap. Extensive experiments on three challenging benchmarks demonstrate that our proposed UASA outperforms state-of-the-art methods by a large margin.