The shipping industry is trying to use new types of fuels to meet strict pollutant emission regulations and carbon emission reduction targets. Hydrogen is one of the options for alternative fuels used in marine applications. Solid oxide electrolysis cell (SOEC) technology can be used for hydrogen production. When water and carbon dioxide are provided to SOECs, hydrogen and carbon monoxide are produced. The interconnector of SOECs plays a vital role in cell performance. In this study, a 3D mathematical model of cathode-supported planar SOECs is developed to investigate the effect of interconnector rib width on the co-electrolysis of water and carbon dioxide in the cell. The model validation is carried out by comparing the numerical results with experimental data in terms of a polarization curve. The rib width is varied from 0.2 mm to 0.8 mm with an interval of 0.1 mm. It is found that the cell voltage is decreased and then increased as the rib width increases. When the current density is 1 A/cm2, the voltages of SOECs with rib widths of 0.2 mm, 0.6 mm, and 0.8 mm are 1.272 V, 1.213 V, and 1.221 V, respectively. This demonstrates that the best performance is provided by the SOEC with a rib width of 0.6 mm. In addition, the local transport processes of SOECs with different rib widths are presented and compared in detail. This study can provide guidelines for the design of interconnectors of SOECs.