LNG carriers have, up to 2006, mainly been driven by steam turbines. The Boil-Off Gas from the LNG cargo tanks has so far been used as fuel. This is a costly solution that requires special skills during construction and operation. Alternative propulsion systems offer far better fuel economical efficiency than steam turbines. Instead of previous practice using Boil-Off Gas as a fuel, the Re-liquefaction system establishes a solution to liquefy the Boil-Off Gas and return the LNG to the cargo tanks. This Re-liquefaction of Boil-Off Gases on LNG carriers results in increased cargo deliveries and allows owners and operators to choose the most optimum propulsion system. In this study, thermodynamic cycle analysis has been performed on two type of LNG Re-liquefaction system which was designed and adopted for the Q-Flex(216,000$m^3$) and Q-Max(266,000$m^3$) LNG carrier under construction at Korea ship yards and variable key factor was simulated to compare efficiency, power and nitrogen consumption of each Re-liquefaction system.