Due to the changeable operating conditions of rotating machinery, the feature distributions of fault are usually changed. Most current cross-domain intelligent fault diagnosis methods only achieve global domain alignment, while ignoring the class discrepancy, resulting in the misclassification of the target domain samples near the class boundary. In this article, a novel joint domain alignment and class alignment (JDACA) method is proposed for cross-domain fault diagnosis of rotating machinery. In JDACA, the strategy of synchronously implementing global domain alignment and class alignment is innovatively proposed. First, a feature extractor and two discrepant classifiers are established to extract high-level features and output predicted results. Then, the maximum mean discrepancy (MMD) loss is used to reduce the marginal distribution discrepancy of high-level features between the source domain and target domain. Finally, the classifier discrepancy loss and the contrastive loss are creatively combined for class alignment learning, which can effectively reduce the conditional probability discrepancy between the source domain and target domain. Moreover, two experiment cases demonstrate the effectiveness of the proposed cross-domain diagnostic method.