The efficient and clean use of fuel is very important for the sustainable development of energy. In this article, a numerical study of molten carbonate fuel cell (MCFC) unit is carried out, and the source, distribution, and extent of six irreversible losses (fluid friction loss, mass transfer loss, ohmic loss, activation loss, heat transfer loss, the coupling loss between heat and mass transfer) are described and quantified. The effects of the operation temperature, current density, CO2 concentration, and cathode CO2 utilization rate on the exergy destruction and exergy efficiency during the power generation process are investigated. The results show that the main source of entropy generation in MCFC is the potential difference, which affects the ohmic and activation entropy generation, especially when the CO2 concentration is very low. The second is the temperature gradient, which causes the entropy production of the heat transfer. With the rise of the CO2 concentration at the cathode inlet, the exergy destruction reduces and the exergy efficiency increases. With the rise of the cathode CO2 utilization rate, the exergy destruction rises and the exergy efficiency reduces. Therefore, analyzing the irreversible process transfer mechanism in MCFC can provide the theoretical basis for its thermal performance optimization and structure design.