Reliable and precise parameters' identification of the solid oxide fuel cell (SOFC) models is vital for the simulation and analysis of its steady-state and dynamic behaviors. However, the SOFC model is characterized by multimodal, high nonlinearity, and strong nonconvexity natures. Therefore, this paper develops a novel variant of the chameleon swarm algorithm (CSA), named memory-based chameleon swarm algorithm (MCSA), to extract highly accurate and precise parameters of SOFC model. In the MCSA, the search mechanism of the chameleon is guided using an internal memory to keep track of the best solutions in previous generations using neighborhood searching strategy, experience-based crossover scheme, and greedy selection strategy. These strategies can provide an appropriate balancing among the global exploration and local exploitation phases. Besides, the stored solutions in the memory can enhance the population diversity and accordingly increase the propensity of reaching the global optimal efficiently. The proposed MCSA is examined on various scenarios of the SOFC model under the steady-state and dynamic state manners. The simulation results of the proposed algorithm are confirmed and validated via comprehensive comparisons using the statistical measures and Friedman nonparametric test with other recent counterparts. The conducted comparisons and analyses have affirmed the efficacy and superiority of the proposed MCSA through achieving accurately identified parameters, where minimum deviation among the estimated and measured stack current-voltage and stack current-power curves is exhibited.