Based on the current models of phosphoric acid fuel cells (PAFCs) and thermoelectric generators (TGs), a new hybrid system is proposed, in which the effects of multi-irreversibilities resulting from the activation, concentration, and ohmic overpotentials in the PAFC, Joule heat and heat leak in the TG, finite-rate heat transfer between the TG and the heat reservoirs, and heat leak from the PAFC to the environment are taken into account. Expressions for the power output and efficiency of the PAFC, TG, and hybrid system are analytically derived and directly used to discuss the performance characteristics of the hybrid system. The optimal relationship between the electric currents in the PAFC and TG is obtained. The maximum power output is numerically calculated. It is found that the maximum power output density of the hybrid system will increase about 150 Wm(-2), compared with that of a single PAFC. The problem how to optimally match the load resistances of two subsystems is discussed. Some significant results for practical hybrid systems are obtained. (C) 2015 Elsevier B.V. All rights reserved.