This paper develops a novel peafowl (Pavo muticus/cristatus) optimization algorithm (POA), which contains its design, evaluation, and application in solid oxide fuel cell (SOFC) parameter estimation. POA mainly replicates the courtship, foraging, and chasing behaviors of peafowls swarm, in which three types of peafowls, i.e., peacocks, peahens, and peafowl cubs are employed to mimic the dynamic swarm behaviors and hierarchy during food searching. Particularly, effective and efficient exploratory and exploitative searching operators are implemented, i.e., food searching and unique rotation dancing behaviors of peacocks, as well as adaptive searching and approaching mechanism of peahens and peafowl. Two widely applied SOFC models, i.e., electrochemical model and steady-state model are adopted for validation under different operation conditions. Simulation results demonstrate that POA outperforms its competitors, e.g., particle swarm optimization (PSO), grey wolf optimization (GWO), ant lion optimization (ALO), and dragonfly algorithm (DA). For instance, under the validation on 79 cells based stack of electrochemical model, RMSE obtained by POA is only 0.42%, 0.27%, 2.05%, and 3.99% to that of ALO, DA, GWO, and PSO, respectively. In addition, 23 standard benchmark functions are used for analysis, experimental results show that POA can effectively explore desirable searching areas and locate the global optimal solutions. The source code of POA is publicly availabe at https://www.mathworks.com/matlabcentral/fileexchange/102809-peafowl-pavo-muticus-cristatus-optimization-algorithm.