Spider-web hierarchy can be introduced by adding smaller hexagons at the centers of original cells in an underlying hexagonal network and connecting the adjacent vertices by straight beams. To examine the out-of-plane crashworthiness of this new type of hierarchical honeycomb concept, a finite element model is established and validated by existing theoretical and experimental results. Then, a parametric study on structural variables ${\gamma }_1$ and ${\gamma }_2$ was carried out with three different densities. The mechanical properties of hierarchical honeycombs are also compared with that of regular honeycombs. The research results show that the deformation patterns of hierarchical honeycombs can be divided into three categories. The energy absorption capability can be controlled effectively by proper adjustment of the hierarchical structural parameters. The specific energy absorption per unit mass ($SE{A}_m$ ) of first-order spider-web hierarchical honeycomb with ${\gamma }_1=\text{0}\text{.8}$ and second-order spider-web hierarchical honeycomb with ${\gamma }_1=\text{0}\text{.8}$ and ${\gamma }_{\text{2}}=\text{0}\text{.65}$ increases by 62.1% and 82.4%, respectively. Meanwhile, the spider-web hierarchical characteristics have less influence on the corresponding Peak Crushing Force (PCF). Further, the mean crushing force is derived by dividing the profile into basic angle elements based on the Simplified Super Folding Element (SSFE) method. The theoretical calculation is in good agreement with the simulation results as the spider-web hierarchical honeycombs deform in Mode I. These results can provide valuable suggestions in the study and design of the new type hierarchical honeycombs.