Because environmentally-friendly fuels such as natural gas and hydrogen are primarily stored in the form of cryogenic liquids to enable efficient transportation, the demand for cryogenic fuel (LNG, LH) ships has been increasing as the primary carriers of environmentally-friendly fuels. In such ships, insulation systems must be used to prevent heat inflow to the tank to suppress the generation of boil-off gas (BOG). The presence of BOG can lead to an increased internal pressure, and thus, its control and prediction are key aspects in the design of fuel tanks. In this regard, although the thermal analysis of the phase change through a finite element analysis requires less computational time than that implemented through computational fluid dynamics, the former is relatively more error-prone. Therefore, in this study, a cryogenic fuel tank to be incorporated in ships was established, and the boil-off rate (BOR), measured considering liquid nitrogen, was compared with that obtained using the finite element method. Insulation material with a cubic structure was applied to the cylindrical tank to increase the insulation performance and space efficiency. To predict the BOR through finite element analysis, the effective thermal conductivity was calculated through an empirical correlation and applied to the designed fuel tank. The calculation was predicted to within 1% of the minimum error, and the internal fluid behavior was evaluated by analyzing the vertical temperature profile according to the filling ratio.