The solid oxide fuel cell (SOFC) is regarded as one of the most promising green power generation technologies because of its characteristics of high conversion efficiency, no pollutant emission and low operating noise. It is widely used in power systems, transportation and other fields. This paper proposes a parameter extraction framework for SOFCs based on the chaos game optimization (CGO) method, which addresses the parameter optimization design problem of SOFC steady-state models. In-depth research and analysis have been conducted on the performance of parameter extraction using the proposed framework, the dandelion optimizer (DO), the equilibrium optimizer (EO), the particle swarm optimization (PSO) algorithm, and the white shark optimizer (WSO) for experimental data of ceramic anode-supported planar low-temperature single-cell fuel cells (ASC-400B) produced by the Finnish fuel cell technology company Elcogen operating at two different temperatures (i.e., 600 ℃ and 700 ℃), as well as simulation data from a 5 kW-level tubular SOFC stack model developed based on physical models by Montana State University, also at two different temperatures (i.e., 850 ℃ and 950 ℃). The test results indicate that compared to DO, EO, PSO, and WSO, CGO can accurately, stably, and rapidly extract the model unknown parameters of various SOFCs mentioned above, providing an efficient method for system modeling of SOFCs.