Proton exchange membrane fuel cells (PEMFCs) have been known to be a feasible method for sustainable power generation to meet the ever-increasing electricity demand with no greenhouse gases emission. Thus, under varying operating circumstances, the PEMFCs have gained considerable importance as an alternative energy source. The optimal operation of PEMFC needs to be ensured to exploit its advantages to the maximum limit. In this direction, there is an extensive need for parameter extraction of PEMFC. Many researchers have applied evolutionary optimization approaches to estimate the PEMFCs parameters as the precise modeling of these cells are not possible. To optimize unknown parameters of PEMFCs, a metaheuristic algorithm is proposed, that is, chaotic mayfly algorithm (CMA) is being proposed in this manuscript. The model's statistical effects are more aligned with the actual experimental findings, according to an experimental finding. The results so obtained suggest that CMA variants are a valuable and efficient method of estimating the parameters of PEMFCs models. Even the nonparametric tests like the Friedman ranking test, Wilcoxon's rank-sum test, and Mood's median test suggest that the proposed algorithm shows better accuracy of the extracted parameters as compared to the other algorithms namely considered in this work.