A novel model of the hybrid system consisting of a SOFC (solid oxide fuel cell) and a vacuum TIG (thermionic generator) is proposed so that the high temperature waste heat produced in the fuel cell can be efficiently exploited. Analytic expressions for the power outputs and efficiencies of the SOFC, TIG, and hybrid system are derived. The relation among the current density of the SOFC, the voltage output of the TIG, and the ratio of the areas of the SOFC and TIG is obtained by the energy balance equation. The influence of the current density of the SOFC on the power output density and efficiency is discussed for a given ratio of areas or voltage output. The maximum power output density and efficiency of the hybrid system are, respectively, equal to 0.560 W/cm(2) and 0.284 and the efficiency of the hybrid system at the maximum power output density is 0.240. The optimal regions of the power output and efficiency of the hybrid system are determined. The advantages of the hybrid system are expounded, compared with the single SOFC. (C) 2015 Elsevier Ltd. All rights reserved.