An electrochemical model was developed to simulate the J-V characteristics of a solid oxide steam electrolyzer (SOSE) used for hydrogen production. Activation, concentration, and ohmic overpotentials were considered as the main factors for voltage loss. The Butler-Volmer equation, Fick's model, and Ohm's law were applied to determine the overpotentials of a SOSE cell. The simulation results were compared with experimental data from the literature and good agreement was obtained. Additionally, parametric modeling analyses were conducted to study how the operating temperature and gas composition affected the electrical characteristics. It was found that the voltage loss could be reduced by increasing the operating temperature and steam molar fraction. It was also observed that an anode-supported SOSE cell exhibited a higher hydrogen production efficiency than electrolyte-supported and cathode-supported cells. The electrochemical model can be used to perform further analysis in order to further understand the principles of SOSE hydrogen production, and to optimize SOSE cell and system designs.