Additive manufacturing provides great geometrical freedom for fabricating structures with complex or customized architecture. One of the applications benefiting from this technology is the fabrication of functionally graded materials with high degree of control of internal architecture which can be strategic application in advanced energy absorption. This study aims to explore the mechanical properties of functionally graded lattice structures fabricated by an additive manufacturing technique namely, selective laser melting (SLM), with Ti-6Al-4V as the building material. Both cubic lattice and honeycomb lattice structures with varied strut diameter and density were designed and manufactured, and their physical characteristics, deformation behavior and compressive properties were investigated. The collapse of structure always started from least dense layer to the denser layers. In contrast, samples with uniform density showed abrupt shear failure with diagonal cracking across the whole structure. The plateau stress and specific energy absorption of density graded samples were higher than for uniform density samples for three out of four designs by up to 67% and 72%, respectively. In addition, density graded lattices showed distinct energy absorption behavior with cumulative energy absorption increasing as a power of strain function while uniform density lattices showed a near-linear relationship. Display omitted •New designs of functionally graded material with continuous density change were investigated.•The designs were opposed to those reported in literature with abrupt change.•The designed structures were shown to have novel deformation behavior than homogenous counterparts under compression.•Plateau stress and specific energy absorption of the structures were higher than homogenous counterparts for most designs.