A new fossil fuel utilized high performance combined power generation system with liquefaction recovery of carbon dioxide is proposed. In the system, pure oxygen is used as the oxidant gas to prevent the mixture of nitrogen in the exhaust gas and to make the liquefaction recovery of carbon dioxide possible. A solid oxide fuel cell (SOFC) is selected as the topping cycle. The exhaust fuel gas of the SOFC is afterburned with its exhaust oxidant gas of pure oxygen, and the heat of the combustion gas is utilized in the bottoming cycle. A closed cycle MHD/noble gas turbine cycle is selected as the bottoming cycle because the temperature of the combustion gas reaches about 2300 K. It is made clear through detailed examination of the energy balance that the total thermal efficiency of the system using natural gas (methane) as the fuel reaches 63.66% (HHV) or 70.64% (LHV). This efficiency is very high for the system with carbon dioxide recovery. The proposed system, therefore, has excellent performance and is worth further research and development.