This paper proposes a novel robust prognostic approach that contains three phases for degradation prediction of proton exchange membrane fuel cell (PEMFC) performance and its remaining useful lifetime (RUL) estimation. In the first detrending phase, a physical aging model (PAM) is used to remove the non-stationary trend in the original fuel cell degradation data. In the second filtering phase, the order of autoregressive and moving average (ARMA) model is determined by autocorrelation function (ACF), partial ACF and Akaike information criterion. The linear component in the stationary time series is then filtered by the identified ARMA model. In the third prediction phase, the remaining nonlinear pattern is used to train the time delay neural network (TDNN), in order to provide the final prediction result. Since the proposed prognostic approach uses appropriate methods to analyze and preprocess the original degradation data (i.e., the PAM maintains stationary trend, and then the identified ARMA filters linear component), the remaining nonlinear pattern of stationary time series can thus guarantee a good convergence performance of TDNN. In order to experimentally demonstrate the robustness and prediction accuracy of the proposed approach, degradation tests are performed using two types of PEMFC stack.