With the development of science and technology, hyperspectral image (HSI) classification has been studied in depth by researchers as one of the important means of human cognition in living environments and the exploration of surface information. Nevertheless, the shortage of labeled samples is a major difficulty in HSI classification. To address this issue, we propose a novel HSI classification method called class-weighted domain adaptation network (CWDAN). First, the convolutional domain adaption network (ConDAN) is designed to align the marginal distributions and second-order statistics, respectively, of both domains via multi-kernel maximum mean discrepancy (MK-MMD) and CORAL loss. Then, the class-weighted MMD (CWMMD) is defined to simultaneously consider the conditional distribution discrepancy and changes of class prior distributions, and the CWMMD-based domain adaptation term is incorporated into the classical broad learning system (BLS) to construct the weighted conditional broad network (WCBN). The WCBN is applied to reduce the conditional distribution discrepancy and class weight bias across domains, while performing breadth expansion on domain-invariant features to further enhance representation ability. In comparison with several existing mainstream methods, CWDAN has excellent classification performance on eight real HSI data pairs when only using labeled source domain samples.