In order to further improve the bending performance of the traditional re-entrant (RE) honeycomb, a novel auxetic honeycomb architecture, called RE-L honeycomb, was proposed by adding an additional link-wall structure to the RE cell. The bending behaviors of the novel RE-L honeycomb, including the properties under linear elastic deformation and the bending behaviors under large deformation, were comprehensively investigated by the analytical, numerical, and experimental models. Results show that the proposed RE-L honeycomb significantly improves the bending compliance in the x-direction due to the highly flexible performance of the additional structure, where the bending rigidity and the maximum bending force are only 23% and 29.4% of those of the RE honeycomb, respectively. Besides, the additional structure obviously improves the designability and orthotropic properties of the original auxetic honeycomb. In conclusion, the proposed RE-L shows improved bending performance, which deserves more attention in future research and related applications.