Lightweight auxetic reentrant honeycombs (ARH) with negative Poisson's ratio (NPR) are very promising for crashworthiness applications due to high specific-strength and energy-absorption (EA). To dig up the potential of ARH, a bio-inspired self-similar “concentric auxetic reentrant honeycomb (CARH)” is proposed to reinforce the EA. Finite element model is established and verified via available reference results for quasi-static-, low-, medium- and high-velocity compression. Two types of CARHs including CARH-I and CARH-II are designed to systematically explore the crashworthiness. The quasi-static and dynamic compression behaviors and EA characteristics are compared among different structures. There is a harvest that the bio-inspired CARHs show higher plateau stress and EA than the traditional ARH, while CARH-II > CARH-I. To clearly understand strengthening mechanisms, different global and unicellular shrinkage deformation modes (e.g., “x”, “X”, “I”, “V”, etc.) are revealed under different velocities. Summarily, the enhancement is due to coupling deformation and energy-dissipation of more plastic-hinges. The horizontal strain of each layer is studied to reveal the NPR effect, which shows a significant velocity effect on the horizontal strain. From parametric studies, typical parameters (e.g. wall-thickness, distance and number of concentric walls) have considerable effects on crashworthiness of CARH. The present bio-inspired design and findings offer a reference for the development of honeycomb with special functions.