Graded triple periodic minimal surface (TPMS) structures fabricated by selective laser melting (SLM) are superior candidates for lightweight and energy-absorbing applications. Previous studies have reported that TPMS structures with a constant wall thickness showed excellent performance; however, exploring the properties of TPMS structures with a graded thickness remains a challenge because of the lack of design theory. This study proposes a novel method for the design of graded-thickness TPMS structures. The manufacturability, mechanical properties and energy absorption capacities of Ti6Al4V graded samples are summarised and compared for different thicknesses and TPMS types. The findings reveal that manufacturing accuracy is influenced by the designed thickness and overhang angle. The constant-thickness TPMS samples exhibited good stiffness, strength and energy absorption capacities, while the graded-thickness samples avoided large stress fluctuations and showed higher elastic moduli and cumulative energy absorption values than the constant-thickness samples. The local curvature distribution also predicted the deformation behaviour of the TPMS structures. This graded-thickness modelling method offers a new perspective on porous structure design, and the experimental results indicate the importance of selecting the proper unit type and graded parameters for most applications.