Based on the face-centered cubic structure, several different types of cubic lattice structures are designed in this paper, the quasi-static compression behavior of the lattice structure is thoroughly investigated by finite element simulation and experimental testing, in which mechanical properties and energy absorption capacities are summarized. The experimental specimens made from thermoplastic polyurethane TPU are additively manufactured using the fused deposition technology. Effects of strut style, strut distance, arrangement form, curvature, and several honeycomb lattice structures are considered. The results show that: under the condition of the same relative density, the selection of sinusoidal struts with larger curvature, the arrangement of 45°/135°, and the inward gradient of the strut distance can all improve the energy absorption characteristics of the structure. Compared with the traditional face-centered cubic structure (specimen L-1), the SEA of the structure with the strut curvature of 0.25, the 45°/135° arrangement of the sinusoidal struts, and the inward gradient of the strut distance is improved by 64% , 190%, and 107%; the introduction of a honeycomb structure with a high relative density can effectively resist the buckling deformation of the structure, and the SEA of the triangular, re-entrant and hexagonal honeycomb structures are 354%, 603% and 548% higher than that of the basic structure, respectively. In addition, reducing the lattice height also resists destabilization.