As ordered cellular materials, lattice materials are excellent lightweight candidates for impact energy/shock absorbing applications. This study aims to explore an advanced lattice material with objective of maximum energy absorption based on topology optimisation. Effects of cell-wall material and mass fraction on topological results are analysed. Generally, a cuttlebone-like lattice (CLL) material is obtained and its deformation behaviour and compressive properties under impact loads are investigated. The results show that the CLL material undergoes a buckling-dominated and layer-by-layer deforming process, irrespective of cell-wall materials and relative densities. The compressive properties of the as-designed lattice material versus relative density can be described by the Gibson-Ashby power law. Impressively, the CLL material outperforms a broad range of existing cellular materials in terms of relative collapse strength, relative elastic modulus and specific energy absorption, which are significantly enhanced by 141.96%, 203.01% and 174.06%, respectively, comparing with Octet lattice material. It is expected that this newly designed lattice material with tailored mechanical properties can act as an excellent impact energy/shock absorber.