In order to impprove the protective effect of the automotive energy absorption (EA) box, the design of the reentrant bioinspired EA box is proposed, that is, novel bioinspired structures are inserted into the original EA box to improve the EA effect of the box. The improved bionic structures with curvature are designed according to the spider web: honeycomb structure (HS), arc-honeycomb structure (AHS), negative Poisson structure (PS), and arc negative Poisson structure (APS). A new bionic automobile energy absorbing box is constructed by combining with automobile energy absorbing box. Experiments and simulations further verify excellent mechanical properties of bionic structures. The results show that EA of AHS and APS is 117.2% and 105.8% of HS and PS. Their specific energy absorption is 112.2% and 102.7% of HS and PS. HS EA box structure, AHS energy absorption box structure, PS energy absorption box structure, and APS energy absorption box structure are 114.2%, 117%, 109.2%, and 116.2% higher than traditional EA box structures, respectively. The excellent characteristics of biological structures can provide ideas for structural design objectives of engineering applications and greatly simplify the process of optimal design.