Energy-dissipating structures are widely used in automotive and aerospace engineering. Novel design for energy-dissipating structures using gradient auxetic cellular material is proposed. The structure is built by layers of auxetic cellular units with varying heights. Compared with cellular structure with uniformly sized cells, the gradient structure has lower resistant force together with better energy absorption ability. A crash box for low-speed collision is designed with the proposed pattern. Optimisation to minimise the mass of crash box with constrains on the crash-resistant force and energy absorption is conducted. Validations with standard collision tests are carried out and results show the obtained structure with gradient auxetic cellular structure passes the test and performs effectively as an energy dissipating structure.