The working process of solid oxide fuel cells (SOFCs) includes at least heat-up, start-up, operating and cool-down steps. In the start-up process, it is necessary to ensure SOFCs work under a steady-state with an external load since considerable energy loss is induced by instable thermal expansion. In this study, the polarization of fuel cells induced by thermal expansion in the start-up process is investigated analytically. The results indicate that the electrode thickness change induced by thermal expansion and the temperature-dependent effective binary diffusivity substantially impact the energy loss. The polarization induced by thermal expansion is dependent on both output current density and operating temperature. Our work facilitates accurate evaluation of cell polarization and efficient operation of SOFCs with decreased energy loss during the start-up stage.