Cycle analysis was performed in order to find the optimum design point of the LNG Boil-off gas re-liquefaction system. Thermodynamic analysis revealed the system could be defined by three state variables. Thus the system performance could be described by the three cold endpoint temperatures of the three-pass heat exchanger. This enabled us to investigate the cycle performance in terms of the heat exchanger parameters. To get access to the cycle states of higher system performances, larger heat exchangers were found necessary. Also the thermal pinch in cryogenic heat exchangers was found to act as a limiting factor to the system performance.