Abstract The model of a new molten carbonate fuel cell (MCFC) system is established, in which multi-irreversibilities resulting from the anode, cathode, and ohm overpotentials are taken into account. Based on thermodynamic-electrochemical analysis and the semi-empirical equations available in literature, expressions of some main parameters such as the cell voltage, power output, efficiency and entropy production rate are derived. The influence of the gas inlet compositions on the electrode overpotentials is discussed in detail. It is found that there exist the optimal anode CO2 concentrations for different anode H2 concentrations. The performance characteristic curves of the MCFC system are represented through numerical calculation and the optimal operation regions of the main parameters are determined. Moreover, a new multi-objective function is used to further optimize the characteristics of the MCFC system, and consequently, the important problem of how to give consideration to both the efficiency and power output in the optimal operation region of the system is expounded.