Developing highly efficient thermodynamic cycles is of great importance in the area of distributed energy system, there are still many non-negligible problems on feasibility assessment and performance evaluation in the application of some emerging technologies, especially involving the fuel cells and carbon dioxide power cycles. This study proposes a distributed heat and power cogeneration system composed of a solid oxide fuel cell, a gas turbine, a steam Rankine cycle, a supercritical carbon dioxide Brayton cycle, and a heat exchanger. The system mathematical model is constructed, and the investigation on system energy, exergy, economic, environmental, and techno-economic performance is performed to demonstrate the technology’s feasibility and applicability. The simulation results indicate that the system can provide 367.03 kW of power and 58.02 kW of heating at the design point, and the overall electrical, exergetic, and energy efficiencies are 68.38 %, 72.41 %, and 79.19 %. The total cost rate of system is achieved to be 11.62 $/h with the system carbon dioxide emission and payback period being 0.2829 kg/kWh and 10.87 year. It can be concluded from the sensitivity analysis that the increases of the compressor pressure ratio, fuel flow rate, and SOFC inlet temperature contribute to improving the system electrical efficiency, while the carbon dioxide emission and the payback period can be reduced. Finally, multi-objective optimization of the cogeneration system is further performed to provide a strategy of performance improvement for system designers and decision makers. The optimization result indicates that though the system carbon emission is increased by 0.25 %, the system payback period and levelized cost of energy are obtained to be 9.88 year and 0.2836 kg/kWh, which are decreased by 9.11 % and 1.47 % compared to the design point.