The LNG carriers have been propelled by steam turbines and the LNG boil-off(BOG) has been used as fuel or vented. However, as the alternative propulsion systems such as diesel engines are being equipped on the LNG carriers for better fuel efficiency, a need for the LNG BOG re-liquefaction system that liquefies the BOG and sends the liquid BOG back to the LNG cargo has arisen in recent years. This study investigates the design of the BOG re-liquefaction system based on the reverse Brayton refrigeration cycle. The thermodynamic and heat exchanger analysis are carried out and the limitations to the system performance are discussed.