<p>Triply periodic minimal surface (TPMS) structures, characterized by special repeating 3D surface periodically with an average curvature of zero in three-dimensional directions, have a wide range of applications. Laser powder bed fusion (LPBF) technique, as a type of additive manufacturing techniques, provides the capability to fabricate such complex-shaped porous TPMS structures. In this study, Ti6Al4V G-sheet TPMS structures with various unit cell sizes were fabricated using LPBF to investigate the structural and material anisotropy and their effects on the anisotropy in energy absorption capacity by combining the finite element simulations and experimental analysis. The results showed that the TPMS structures can be successfully fabricated using LPBF, although the sheet thickness exceeds the designed values, with deviation decreasing as the unit cell size increases from 2 to 4 mm. The inherent anisotropy during the LPBF process results in variations in structural dimension, materials characteristics, and energy absorption capacity between directions parallel and perpendicular to the build direction. The anisotropic ratio of the LPBFed Ti6Al4V G-sheet TPMS structures increases from 1.5 to 2.2 in the structural dimension and from 2.8 to 3.3 in specific energy absorption per unit mass (SEA_m) respectively with decreasing the unit cell size from 4 to 2 mm. The anisotropy of SEA_m primarily originates from the coupling effects of anisotropic dimensions and material properties in the LPBFed G-sheet TPMS structure. Among these factors, anisotropic material properties play a more significant role compared to dimensional anisotropy.</p> Graphical abstract <p></p>