© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.Many significant parameters show the performance of batteries used in important fields such as biomedical systems, energy storage units, electric vehicle technologies, and advanced space studies. Two essential indicators among these parameters are open-circuit voltage and state of health. In this study, it is tried to estimate open-circuit voltage and state of health with high accuracy by applying optimization methods on the Thevenin electrical equivalent circuit model of batteries. The parameter values obtained by examining the discharge tests of the Li-ion battery cell with 2A constant current during the 150 charge/discharge cycle time at 25 °C are transferred to the electrical equivalent circuit model. Curve-fitting method, artificial bee colony, particle swarm optimization, dragonfly algorithm, and genetic algorithm have been studied in the prediction operation of open-circuit voltage and state of health which is defined based on state of charge, number of cycles, rated current capacity, and time. Comparisons are made considering the absolute error values, the smallest value of the sum of the squares of the errors, the response speed of the methods, and the correct estimation ability. Ultimately, it is aimed to obtain the most suitable method.