Besides electricity generation, solid oxide fuel cells (SOFCs) produce a significant amount of waste heat, which needs to be immediately removed to ensure the normal operation of SOFCs. If the waste heat is recovered through bottoming thermal devices, the global efficiency of SOFCs can be improved. In this study, a new hybrid system mainly consisting of a thermoelectric generator, a thermoelectric cooler and an SOFC is proposed to recover the waste heat from SOFC for performance enhancement. The thermodynamic and electrochemical irreversible losses in each component are fully considered. An analytical relationship between the SOFC operating current density and the thermoelectric devices dimensionless electric current is derived, from which the range of SOFC operating current density that permits the thermoelectric devices to effectively work is determined. The equivalent power output and efficiency for the hybrid system are specified under different operating current density regions. The feasibility and effectiveness are illustrated by comparing the proposed hybrid system with the stand-alone SOFC. It is found that the power density and efficiency of the proposed system allow 2.3% and 4.6% larger than that of the stand-alone SOFC, respectively. Finally, various parametric analyses are performed to discuss the effects of some design and operation parameters on the hybrid system performance. (C) 2017 Elsevier Ltd. All rights reserved.