This study is basically composed of two sections. In the first section, a CFD analysis is used to provide a better insight to molten carbonate fuel cell operation and performance characteristics at very high current densities. Therefore, a mathematical model is developed by employing mass and momentum conservation, electrochemical reaction mechanisms and electric charges. The model results are then compared with the available data for an MCFC unit, and a good agreement is observed. In addition, the model is applied to predict the unit cell behaviour at various operating pressures, temperatures, and cathode gas stoichiometric ratios. In the second section, a thermodynamic model is utilized to examine energy efficiency, exergy efficiency and entropy generation of the MCFC. At low current densities, no considerable difference in output voltage and power is observed; however, for greater values of current densities, the difference is not negligible. If the molten carbonate fuel cell is to operate at current densities smaller than 2500 A m-2, there is no point to pressurize the system. If the fuel cell operates at pressures greater than atmospheric pressure, the unit cell cost could be minimized. In addition, various partial pressure ratios at the cathode side demonstrated nearly the same effect on the performance of the fuel cell. With a 60 K change in operating temperature, almost 10% improvement in energy and exergy efficiencies is obtained. Both efficiencies initially increase at lower current densities and then reach their maximum values and ultimately decrease with the increase of current density. By elevating the pressure, both energy and exergy efficiencies of the cell enhance. In addition, higher operating pressure and temperature decrease the unit cell entropy generation.