Abstract: This study proposes a new type of cosine function cell-based (CFCB) lattice materials and conducts experimental and simulation studies on the mechanical properties of such materials under quasi-static out-of-plane compressive load. The experimental results show that the energy absorption of the CFCB lattice material is improved by 134.4% compared with that of the body centered cubic (BCC) lattice material. Besides, through numerical simulation, it is found that the energy absorption of CFCB lattice materials increases with the increase of the diameter of the single-cell diameter. In order to further improve the out-of-plane compression deformation mode and improve the bearing performance of uniform CFCB lattice materials, an interlayer gradient CFCB lattice material was designed, and energy absorption capacity of these gradient lattice materials and their key affecting factors are experimentally and numerically investigated. The results show that the gradient CFCB lattice materials have superior advantages in energy absorption compared with uniform CFCB lattice materials, and it is also found that increasing gradient coefficients can improve their load-bearing capacity and energy absorption capacity. Finally, the multi-objective discrete optimization method was used to optimize the design of the interlayer gradient CFCB lattice material, and the specific energy absorption of the optimized gradient CFCB gradient lattice material was improved by 35.3%, and the energy absorption was increased by 7.1%. This study can provide reliable experimental results, accurate numerical models and efficient optimization methods for the design of novel CFCB lattice materials and their gradient configurations.