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This paper introduces the application of the variants of the Grey Wolf Optimisation algorithm for the sake of assessing unknown parameters of Proton Exchange Membrane Fuel Cells models. Three versions of Grey Wolf Optimisation algorithm are applied: Conventional Grey Wolf Optimisation, Improved Grey Wolf Optimisation based on dimension learning-based hunting, and Selective Opposition-based Grey Wolf Optimisation. Moreover, Optimisation algorithms of Ant Lion Optimiser, Atom search optimisation, Dragonfly algorithm, and Multi-Verse Optimiser have been applied to estimate the parameters of Proton Exchange Membrane Fuel Cells models for the validation purpose. These algorithms are applied to three commercial Proton Exchange Membrane Fuel Cells stacks: BCS 500W-PEM, 500W-SR-12PEM and 250W-stack. The analyses are executed considering several operational circumstances. Sum of square errors value of the results based on parameters estimation and those experimentally tested are calculated. The objective function is chosen as sum of square errors value. The results are compared with those obtained using well-known methods in the literature to validate the effectiveness of the proposed methods. It is noticeable that the simulated I-V curves momentously match the datasheet curves for all the studied cases. In addition, considering the accuracy of the solution and the convergence speed, the Proton Exchange Membrane Fuel Cells model based on the Improved Grey Wolf Optimisation algorithm excels all other algorithms. Based on the simulation results, the Improved Grey Wolf Optimisation algorithm can improve the optimisation efficiency to 99.97 for the 250 W stack while the efficiency with Grey Wolf Optimisation and Selective Opposition-based Grey Wolf Optimisation are 98.83 and 98.84, respectively, for the 250 W stack case study.