Three-phase induction motors (TPIMs) are prone to numerous faults due to their complicated stator and rotor conditions and require a fast response, accurate, and intelligent diagnostic system. Recently developed fault diagnostic systems for induction motors are based on machine learning approaches, but their complex structure typically results in long training time. Moreover, they need to be retrained from scratch if the system is not accurate. We apply incremental broad learning (IBL) method to the diagnosis of TPIM faults. The IBL can train and retrain the network efficiently due to its flexible structure. The new diagnostic framework also consists of feature extraction techniques (empirical mode decomposition and sample entropy) and a non-negative matrix factorization (NMF) IBL approach. The experimental results demonstrate that the IBL system is superior to some algorithms, such as deep belief networks, convolutional neural networks, and extreme learning machine. Moreover, the IBL simplified by NMF is more accurate than the IBL without NMF.