This paper proposes a new type of Gas Turbine Cycle-supercritical CO2 Brayton/organic Rankine cycle (GT-SCO2/ORC) cogeneration system, in which the exhaust gas from gas-fired plants generates electricity through GT and then the remaining heat is absorbed by the supercritical CO2 (SCO2) Brayton cycle and ORC. CO2 contained in the exhaust gas is absorbed by monoethanolamine (MEA) and liquefied via liquified natural gas (LNG). Introducing thermodynamic efficiencies, thermoeconomic analysis to evaluate the system performance and total system cost is used as the evaluation parameter. The results show that the energy efficiency and exergy efficiency of the system are 56.47% and 45.46%, respectively, and the total cost of the product is 2798.38 $/h. Moreover, with the increase in air compressor (AC) or gas turbine isentropic efficiency, GT inlet temperature, and air preheater (AP) outlet temperature, the thermodynamic efficiencies have upward trends, which proves these four parameters optimize the thermodynamic performance. The total system cost can reach a minimum value with the increase in AC pressure ratio, GT isentropic efficiency, and AC isentropic efficiency, indicating that these three parameters can optimize the economic performance of the cycle. The hot water income increases significantly with the increase in the GT inlet temperature, but it is not cost-effective in terms of the total cost.