In this paper, a circuit-based model of proton exchange membrane fuel cell (PEMFC) is developed for optimal selection of the model parameters. The optimization is based on using an improved version of Monarch Butterfly Optimization (IMBO) algorithm for minimizing the Integral Time Absolute Error between the measured output voltage and the output voltage of the achieved model. For validation of the proposed method, two different case studies including 6 kW NedSstack PS6 and 2 kW Nexa FC PEMFC stacks have been employed and the results have been compared with the experimental data and some well-known metaheuristics including Chaotic Grasshopper Optimization Algorithm (CGOA), Grass Fibrous Root Optimization Algorithm (GRA), and basic Monarch Butterfly Optimization (MBO) to indicate the superiority of the proposed method against the compared methods. Final results show a satisfying agreement between the proposed IMBO and the experimental data. (C) 2020 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.