The proton exchange membrane (PEM) fuel cell is considered as one of the promising electrical energy sources, but it suffers from the limited useful lifetime. Prognostics is a good solution to the prediction of the failure occurrence so that actions can be taken to prevent faults in advance. However, the degradation mechanisms are not entirely clear and they are difficult to model, which impedes the development of prognostics applied in PEM fuel cell. The data-driven methods aim at estimating the future behaviors without knowledge of the underlying degradation phenomena. This paper attempts to address the issue and cope with the model uncertainty by the proposed Gaussian process state space-based prognostics, which infers the internal time-varying parameters and the evolution of degradation based on the dynamic model. The degradation trend is presented in a probability distribution and evaluated by a failure probability index for more practical applications. The remaining useful lifetime is deduced when the defined critical threshold is reached. This algorithm is applied to a set of experimental data from a longtime test, and the test results show the effectiveness of the proposed approach. (C) 2018 Elsevier Ltd. All rights reserved.