An accurate prediction of the remaining useful life (RUL) of a proton exchange membrane fuel cell (PEMFC) is of great significance for its large-scale commercialization and life extension. This paper aims to develop a PEMFC degradation prediction method that incorporates short-term and long-term predictions. In the short-term prediction, a long short-term memory (LSTM) neural network is combined with a Gaussian process regression (GPR) probabilistic model to form a hybrid LSTM-GPR model with a deep structure. The model not only can accurately forecast the nonlinear details of PEMFC degradation but also provide a reliable confidence interval for the prediction results. The results showed that the proposed LSTM-GPR model outperforms the single models in both prediction accuracy and confidence interval. For the long-term prediction, a novel RUL prediction model based on an extended Kalman filter (EKF) and GPR is proposed. The GPR model is used to solve the problem that the EKF cannot update the model parameters in the prediction stage. The results showed that the proposed EKF-GPR model can achieve better RUL prediction than the model-based approach and the data-driven approach.