This paper proposes the optimal shape of an LNG fuel tank with a lattice pressure vessel (LPV) design for a tugboat. The LPV is a Type C tank with a design philosophy of “design by analysis,” which facilitates greater variability of shape compared with other traditional Type C tanks. Further, compared with conventional cylindrical fuel tanks, the LPV provides better volumetric efficiency. Considering the shape of a fuel tank room, a trapezoidal shape of the LPV is concluded as the most optimal design. This study performs two major analyses of the LPV: structural and heat transfer analyses. First, a design procedure of the LPV based on structural analyses is elaborated. The finite element method is used for the analyses. Furthermore, the results guarantee that the maximum stresses by applied loads do not exceed an allowable stress limitation. Second, the heat transfer analysis of the LPV is conducted. LNG boil-off gas generation is analyzed based on various insulation materials and the degree of acuum.