Due to the high level of pollutant emissions from traditional marine diesel engines, Liquefied Natural Gas (LNG) as clean energy is becoming a better choice for main engines to replace the traditional fuels. Meanwhile, in order to improve the energy efficiency of the marine power system, the Organic Rankine Cycle (ORC) has been regarded as the most suitable solution to recover the waste heat for the power generation of vessels. In this paper, both the waste heat of the main engine and the cold energy of LNG have been fully considered, and a novel triple ORC process has been proposed for the waste heat and cold energy recovery of LNG-fueled vessels. It adopts the exhaust gas of the main engine and the cooling water from the engine jacket as heat sources, and uses the cold energy of LNG and the sea water as cold sources. Based on the 15 optional working fluid conditions, the heat source utilization rate, system exergy efficiency, net output power, and system cost are, respectively, combined as two objectives, and the multi-objective adaptive firefly algorithm is used to optimize the thermodynamic performance of the system. The optimization results of different heat and cold sources as well as the design parameters have been discussed. Finally, the system's exergy loss has been analyzed to make suggestions for further improvement. The results show that this novel ORC system can better meet the energy recovery requirements of LNG-fueled vessels, with higher net output power, lower cost, and greater energy recovery efficiency. The largest exergy loss of the system exists in the condensers of the stages 2 and 3, and the expanders in the various stages. Therefore, subsequent cooling energy recovery and the use of Stirling engines can be considered to further improve the system efficiency.