The process of constructing a reliable mathematical model of solid oxide fuel cell (SOFC) is a challenge due to its complex nature. This paper proposes a new methodology incorporated a recent meta-heuristic algorithm named parasitism-predation algorithm (PPA) to estimate the optimal parameters of SOFC equivalent circuit. Two experiments are conducted in this work; the first one comprises four measured datasets for a commercial enhanced cylindrical SOFC manufactured by Siemen Energy. While the second series consists of five measured datasets for a theoretical 5ðKWÞ dynamic SOFC stack with 96 connected cells. The collected datasets are measured at different operating conditions. An excessive comparative study is presented with other optimizers of comprehensive learning particle swarm optimization (CLPSO), improved PSO with difference mean with perturbation (DMP_PSO), heterogeneous CLPSO (HCLPSO), locally informed PSO (LIPS), modified CSO with tri-competitive mechanism (MCSO), opposition-based learning competitive PSO (OBLCPSO), ranking-based biased learning swarm optimizer (RBLSO), competitive swarm optimizer (CSO), hybrid Jaya with DE (JayaDE), and social learning PSO (SLPSO). Furthermore, statistical analyses of the ranking tests, multiple sign tests, Friedman tests, and ANOVA are performed. The obtained results confirmed the proposed PPA's competence in constructing a reliable model of SOFC as it provides the least mean square error (MSE) between the measured and estimated characteristics of 2.164e6 in the first series of experiments at 1073 K, in contrast, the most peer (CLPSO) provides 5.57e6. Similarly, in the second series of experiments, PPA achieves lease MSE of 7.17e2 at 973 K; meanwhile, the most peer (CLPSO) attains 5.44e1.