The LNG BOG re-liquefaction system for LNG carriers was designed based on the Claude refrigeration cycle and the thermodynamic analysis was carried out in order to find the design point of the three heat exchangers constituting the system. The thermodynamic analysis revealed that the system state could be defined by the three cold endpoint temperatures of the three-pass heat exchanger. Hence the iso-lines of the specific liquefaction work, taken as the performance indicator, were presented in terms of those three temperatures and discussed. The system was found most economical when those three temperatures approached a single temperature of $-140^{circ}C$ and thus this system state could be taken as the design point for the heat exchangers.