A novel power/cooling cogeneration system integrated with a gas turbine, a supercritical CO2 recompression power system (SCRPC) and a transcritical CO2 power system (TCPC) using liquefied natural gas (LNG) cold energy is proposed and investigated. This new combined system can improve the electrical capacity of gas turbine, and it can maximize the electrical output under different gas turbine load conditions by adjusting the split ratio. A steady-state mathematical model is developed to further understand the performance of the proposed system. It is shown that under the given conditions the combined thermal efficiency and the combined exergy efficiency are 52.94% and 30.27%, respectively. And the exergy analysis shows that the exergy destruction mainly occurs in the combustor, followed by condenser and NG terminal, respectively. Parametric study shows that the engine load conditions, the turbine I inlet temperature, the SCRPC and TCPC highest pressures and the effectiveness of HTR, LTR and regenerator have significant effects on the net work output, the cooling capacity, the combined thermal and exergy efficiencics, and the capital investment cost. Furthermore, multi-objective optimizations considering both thermodynamic and economic aspects are carried out to obtain the Pareto frontier solutions for different multi-objectives, and the optimal design condition is found out by means of the TOPSIS method based on entropy weight. These findings could be helpful in improving the utilization rate of the gas turbine exhaust waste heat and thus boost the system efficiency.