To achieve a fast and low cost diagnostic, we propose a new tool based on wavelet leaders in which the proton exchange membrane fuel cell (PEMFC) diagnosis is made by the observation of the one and only stack voltage. The steps of our strategy are the following ones: (i) the PEMFC is operated under a variety of conditions (nominal or severe) using a characterization test bench developed in lab. The severe operating conditions refer either to single fault types or to different combinations of faults; (ii) the recorded stack voltages are analyzed using a wavelet leader based multifractal analysis (WLMA) in order to identify their singularity spectra as fault signatures. This novel method based on leader discrete wavelet coefficients for the estimation of the singularity spectrum is a well-suited technique for non-stationary and non-linear signals; (iii) a feature selection method is used to select the most relevant singularity features and to remove the redundant ones; (iv) the selected singularity features are classified using Support Vector Machine and K-Nearest Neighbors techniques according to the considered operating situations (faults and combinations of faults).