A hybrid system mainly composed of a DCFC (Direct Carbon Fuel Cell), a TEG (Thermoelectric Generator) and a regenerator is put forward, where the DCFC electrochemically converts the chemical energy in the solid carbon into electricity and waste heat, and the TEG further converts the waste heat into electricity for additional power generation. The main irreversibilities in each element of the hybrid system are characterized, and the heat losses between the DCFC and the environment are also considered. Numerical expressions for the power output and efficiency of the hybrid system are respectively derived, from which the general performance characteristics are revealed. The fundamental relationship between the operating current density of the DCFC and the dimensionless electrical current of the TEG is obtained, and thus the region of the operating current density of the DCFC that the TEG exerts its function is determined. By using such a system, the equivalent maximum power density of the hybrid system allows to be 50% larger than that of the sole DCFC system. The effects of the operating current density, operating temperature, heat conductivity, and some integrated parameters on the performance of the hybrid system are discussed. (C) 2014 Elsevier Ltd. All rights reserved.