The problem of health status prediction of insulated-gate bipolar transistors (IGBTs) has gained significant attention in the field of health management of power electronic equipment. The performance degradation of the IGBT gate oxide layer is one of the most important failure modes. In view of failure mechanism analysis and the easy implementation of monitoring circuits, this paper selects the gate leakage current of an IGBT as the precursor parameter of gate oxide degradation, and uses time domain characteristic analysis, gray correlation degree, Mahalanobis distance, Kalman filter, and other methods to carry out feature selection and fusion. Finally, it obtains a health indicator, characterizing the degradation of IGBT gate oxide. The degradation prediction model of the IGBT gate oxide layer is constructed by the Convolutional Neural Network and Long Short-Term Memory (CNN-LSTM) Network, which show the highest fitting accuracy compared with Long Short-Term Memory (LSTM), Convolutional Neural Network (CNN), Support Vector Regression (SVR), Gaussian Process Regression (GPR), and CNN-LSTM models in our experiment. The extraction of the health indicator and the construction and verification of the degradation prediction model are carried out on the dataset released by the NASA-Ames Laboratory, and the average absolute error of performance degradation prediction is as low as 0.0216. These results show the feasibility of the gate leakage current as a precursor parameter of IGBT gate oxide layer failure, as well as the accuracy and reliability of the CNN-LSTM prediction model.