Bearings prevent damage caused by frictional forces between parts supporting the rotation and they keep rotating shafts in their correct position. However, the continuity of work under harsh conditions leads to inevitable bearing failure. Thus, methods for bearing fault diagnosis (FD) that can predict and categorize fault type, as well as the level of degradation, are increasingly necessary for factories. Owing to the advent of deep neural networks, especially convolutional neural networks (CNNs), intelligent FD methods have achieved significantly higher performance in terms of accuracy. However, in addition to accuracy, the efficiency issue still needs to be weathered in complicated diagnosis scenarios to adapt to real industrial environments. Here, we introduce a method based on multi-output classification, which utilizes the correlated features extracted for bearing compound fault type classification and crack-size classification to serve both aims. Additionally, the synergy of a time–frequency signal processing method and the proposed two-dimensional CNN helped the method perform well under the condition of variable rotational speeds. Monitoring signals of acoustic emission also had advantages for incipient FD. The experimental results indicated that utilizing correlated features in multi-output classification improved both the accuracy and efficiency of multi-task diagnosis compared to conventional CNN-based multiclass classification.