Honeycomb sandwich structures are a common engineering material due to their excellent mechanical properties and crashworthiness. This paper proposes a web-like hierarchical quasi-honeycomb structure inspired by the characteristics of dimensional gradient and layer distribution observed in spider web structures. The out-of-plane load-bearing capacity of the structure is analyzed based on the principle of strain-energy equivalence. Furthermore, multilevel equations for the equivalent elastic and shear modulus are derived. The theoretical derivation is validated by comparing the theoretical analysis with the numerical simulation results. The results show a correlation between the ply factor and the out-of-plane bearing capacity of the structure, which can effectively predict the out-of-plane mechanical properties of the hierarchical structure. Furthermore, when the structure is applied to a traditional pallet, under the same magnitude of force in different directions, the stress and displacement values of the two pallets show minimal change. However, the mass was reduced by 20.9%. This mass reduction demonstrates the potential of the quasi-honeycomb structure for lightweight design and indicates that the structure has a significant potential application prospect in engineering practice.