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This paper presents the design of a re-liquefaction system as a BOG (boil-off gas) handling process in liquid hydrogen transport vessels. The total capacity of the re-liquefaction system was assumed to be 3 ton/day, with a BOR (boil-off rate) of 0.2 %/day inside the cargo. The re-liquefaction cycle was devised using the He-Brayton Cycle, incorporating considerations of BOG capacity and operational stability. The primary components of the system, such as compressors, expanders, and heat exchangers, were selected to meet domestically available specifications. Case studies were conducted based on the specifications of the components to determine the optimal design parameters for the re-liquefaction system. This encompassed variables such as helium mass flow rate, the number of compressors, compressor inlet pressure and compression ratio, as well as the quantity and composition of expanders. Additionally, an analysis of exergy destruction and exergy efficiency was carried out for the components within the system. Remarkably, while previous design studies of BOG re-liquefaction systems for liquid hydrogen vessels were confined to theoretical and analytical realms, this research distinguishes itself by accounting for practical implementation through equipment and system design.