With the increasing demand of energy and urgent need of CO2 emissions reduction, seeking for an approach to achieve carbon capture in a power generation system with high efficiency is a great challenge. Natural gas combined cycle (NGCC) power plants with high power generation efficiency have attracted more and more attention. Oxy-fuel combustion is considered one of the most potential methods for carbon capture in power plants. An integrated system of NGCC and oxy-fuel combustion is proposed to realize the carbon capture in the work. The cold energy of liquefied natural gas (LNG) is utilized to condense CO2 with high efficiency. The simulation of the system is conducted using Aspen Plus. Five kinds of bottom cycle: single pressure (SP) cycle, dual pressure non-reheat (DPN) cycle, dual pressure reheat (DP) cycle, triple pressure non-reheat (TPN) cycle and triple pressure reheat (TP) cycle are established. The oxy-fuel combustion systems considering CO2 and H2O as dilute gas are investigated. The result shows that H2O is not suitable to moderate the combustion temperature in the study case because the latent heat of the flue gas is difficult to release. The efficiency of TP steam cycle is the highest among five kinds of bottom cycle. Taking the power consumption of carbon capture and O-2 production into account, the energy and exergy efficiency of the system with the TP steam cycle is 55.3% and 52.9% respectively. The sensitivity analysis is carried out to study the effects of the flow rate of recycled CO2 and carbon capture pressure on system performance. The results show that with the increase of the amount of recycled CO2, the system power generation decreases. As the CO2 capture pressure increases, the carbon capture rate is elevated, while the CO2 purity drops.