Given the significant emissions from conventional marine diesel engines, many ship owners are increasingly turning to liquefied natural gas (LNG) as a cleaner energy alternative. In this study, a novel power generation system is proposed for LNG-fueled ships, integrating LNG cold energy and waste heat of the main engine, while considering the pressure of LNG. Firstly, this paper compares the two-stage parallel organic Rankine cycle to highlight its superiority. Secondly, the exergy loss and component cost of the system are analyzed, and the influence of these parameters on the thermal economy of the system is discussed. Finally, the multi-objective genetic algorithm is used to select the system exergy efficiency and electricity production cost (EPC), and the optimal performance point of the system is determined. Based on this, the performances of different literature studies are compared, and the system’s potential impact on the environment is evaluated. The results show that the net output power, thermal efficiency, exergy efficiency, EPC, payback period, and CO2 emission reduction of the system are 336.3 kW, 39.38%, 44.38%, 0.043 USD/kWh, 2.68 years, and 21,540 tons, respectively. Therefore, the system provides a new solution for energy saving and emission reduction of ships.