Machine learning models have been widely successful in the field of intelligent fault diagnosis. Most of the existing machine learning models are deployed in static environments and rely on precollected datasets for offline training, which makes it impossible to update the models further once they are established. However, in the open and dynamic environment in reality, there is always incoming data in the form of streams, including new categories of data that are constantly generated over time. In addition, the operating conditions of mechanical equipment are time-varying, which results in continuous stream data that are nonindependently and homogeneously distributed. In industrial applications, the diagnosis problem of nonindependent and identically distributed continuous streaming data is referred to as the cross-domain class incremental diagnosis problem. To address the cross-domain class incremental problem, a novel cross-domain class incremental broad network (CDCIBN) is proposed. Specifically, to solve the nonindependent identically distributed problem, a novel domain-adaptation learning loss function is first designed, which enables the conventional broad network to handle the category increment task well. Then, a cross-domain class incremental learning mechanism is designed, which learns new categories while retaining the knowledge of old categories well enough without replaying old category data. The effectiveness of the proposed method is evaluated through multiple mechanical failure increment cases. Experimental analysis demonstrates that the designed CDCIBN has significant advantages in the variable working condition class incremental application.