This paper studies the coupling of fuel cell power generation technology and conventional thermal power generation technology, constructs the thermodynamic model of combined cycle power generation of fuel cell, gas turbine and steam turbine, and analyzes the thermodynamic performance of the system from the important links such as compressor pressure ratio, steam carbon ratio, fuel utilization, fuel cell operating temperature and gas recirculation. Since natural gas as fuel will emit a lot of greenhouse gases, two new low-carbon power generation systems including composite power system, carbon capture and liquified natural gas cold energy utilization are proposed. In this paper, the post-combustion carbon capture which is more practical and conducive to the safe operation of the system is used. The adsorbents used in the two carbon capture methods are MDEA and CaO respectively. In the MDEA carbon capture process, flash tower and split flow process are added to reduce energy consumption. In the calcium looping carbon capture process, CO2 reflux process is set to optimize the calcination temperature, and two-stage waste heat boilers are set to recover a large amount of waste heat of CO2 and clean flue gas respectively. After that, to further save energy consumption, a method of cascade utilization of liquified natural gas cold energy is proposed. It can not only increase power output, but also provide natural gas at normal temperature and pressure for the system and the outside. The calculation results show that the efficiency of the optimized combined cycle system of fuel cell, gas turbine and steam turbine reaches 70.32%. In terms of energy saving, the system efficiency of MDEA carbon capture process is 1.81% higher than that of calcium looping carbon capture process, and calcium looping carbon capture process has more advantages in economic cost. In addition, the cascade utilization of liquified natural gas cold energy provides additional 410.86 kW, 382.64 kW electric energy and more directly usable natural gas for the two systems. The research results of this paper can provide meaningful guidance for the design of low-carbon and high-efficiency power generation system based on fuel cell.