For hyperspectral image (HSI) classification tasks, obtaining sufficient labeled samples is usually difficult, time-consuming, and expensive. To address the aforementioned issue, by transferring the labeled sample information of a relevant source domain to the unlabeled target domain, an HSI classification method based on the domain adversarial broad adaptation network (DABAN) is proposed. First, the bottleneck adaptation module composed of a bottleneck layer and a domain adaptation layer is constructed and introduced to the domain adversarial neural network; thus, the domain adversarial adaptation network (DAAN) is designed. By simultaneously performing domain adversarial learning, reducing both the marginal distribution difference and second-order statistic difference between two domains, the distributions of the source and target domains are aligned. Then, the conditional distribution adaptation regularization term based on the maximum mean discrepancy is embedded into a broad learning system to obtain the conditional adaptation broad network (CABN). On the one hand, CABN can perform the class-level distribution adaptation on the domain-invariant features extracted by DAAN. On the other hand, the representation ability of the domain-invariant features expanded by CABN can be further enhanced. Experimental results on ten real hyperspectral data pairs show that, compared with the existing mainstream methods, DABAN can effectively utilize relevant source-domain information to assist in improving the classification accuracy of the target domain.