The representative model of fuel cells (FCs) has a vital role in investigating the steady-state and dynamic analysis of these cells. The FC model has a significant impact on simulation studies of such systems and this is appeared in several applications like nano grids, microgrids and smart grids. This manuscript attempts a novel and simplified precise model of the proton electrolyte membrane FCs (PEMFCs). The proposed model deeply reduces the number of unknown parameters of such models to achieve a simplified one. In this regard, it reveals only four design variables within the model. Another salient feature of this study is the novel application of a meta-heuristic algorithm called equilibrium optimizer (K) to obtain these unknown four parameters. The integral squared error criteria is used to formulate the fitness function. The effectiveness of EO-PEMFC model is tested by comparing the simulation with experimental results under various operating situations. The validity of proposed model is also verified by benchmarking its results with that obtained using other optimization-based models. The high efficacy of this model is checked under both steady-state and dynamic operating conditions. With the application of the proposed model, a very precise PEMFC model can be implemented. (C) 2020 Elsevier Ltd. All rights reserved.