In order to improve flywheel reliability, flywheel fault diagnosis technology was studied. A hybrid fault diagnosis method based on a neural network was proposed, which compares the mathematical analysis model with the flywheel fault diagnosis based on intelligent computing. In this method, the difference between the mathematical model and the original system output was used as the first-order residual. Then, the first-order residual and the system measurements were used to train the neural network. Finally, the second-order residual of the mixed model output was used to detect the system fault. This method was validated using the flywheel injection bus voltage and armature current faults. Under the bus voltage fault working conditions, the hybrid model avoided the divergence problem of current estimation because of the analytical model, which reduced the maximum tracking error by 44% compared with a single neural network model. Under the current fault working conditions, the maximum tracking error of the hybrid model was reduced by 90% and the tracking variance was reduced by more than 10 times under different speed conditions compared with two single neural network models. These results illustrate that the hybrid method can effectively solve the problem of inaccurate fault diagnosis due to the existence of modeling errors in the analytical model, as well as the problem of a single neural network model being unable to adapt to fault diagnosis corresponding to new working conditions because of the lack of training data.