Based on the basic nonlinear parameter system of the solid oxide electrolysis cell, the data-driven method was used for system identification. The basic model of the solid oxide electrolysis cell was accomplished in Simulink and experiments were performed under a diversified input/output operating environment. The experimental results of the solid oxide electrolysis cell basic parameter system generated 15 datasets. The system identification process involved the utilization of these datasets with the application of nonlinear autoregressive-exogenous models. Initially, data identification came from the Matlab mechanism model. Then, the nonlinear autoregressive-exogenous structures were estimated and selected exploratively through an individual operating condition. In terms of fitness, we conclude that the solid oxide electrolysis cell parameter system cannot be satisfied by a solitary autoregressive-exogenous model for all datasets. Nevertheless, the nonlinear autoregressive-exogenous model utilized S-type nonlinearities to fit a total of 2 validation datasets and 15 estimated datasets. The obtained results were compared with the basic parameter system of a solid oxide electrolysis cell, and the nonlinear autoregressive-exogenous projected output demonstrated an accuracy of over 93% across diverse operational circumstances—regardless of whether there was noise interference. This result has positive significance for the future use of the solid oxide electrolysis cell to achieve the dual carbon goal in China.