The new energy industry has received extensive attention. The Insulated Gate Bipolar Transistor power module is the core device for new energy equipment, and accurately predicting its remaining useful life (RUL) is conducive to its timely maintenance and replacement, promoting the sustainable development of the society. When the power module fails, its collector–emitter saturation voltage drop () significantly increases. This feature is used to determine RUL of the power module. However, the time series have obvious random non-stationary features. Current methods are ineffective to such features. Therefore, the optimal scale Gaussian process (OSGP) model is proposed. The optimal parameters in the model are determined by Ant Lion Optimizer. The variable-scale function of OSGP model makes it able to handle the randomness and non-stationarity in time series. The results show that OSGP prediction accuracy is higher than that of support vector machine, BP neural network, Gaussian process and Gaussian process mixture. The proposed model has higher prediction accuracy and can adapt to less training samples.