The influence of five geometric parameters of a negative Poisson’s ratio honeycomb structure on the cellular arc angle, length of connecting rod, outer thickness, thickness ratio and length-height ratio were studied. By using uniform test design method, the fitting equations of four evaluation indexes, energy absorption, specific energy absorption, peak crushing force and equivalent Poisson’s ratio were obtained. On this basis, the multi-objective optimization design was carried out, and the appropriate cellular geometric parameters were selected. The results show that the cellular arc angle and the length of the connecting rod have great influence on the specific energy absorption of the honeycomb structure, the outer thickness and thickness ratio have great influence on the peak crushing force and energy absorption of the structure, However, the outer thickness under equal strain has little effect on the equivalent Poisson’s ratio of the structure. The energy absorption and equivalent Poisson’s ratio of the structure are greatly affected by the length-height ratio. Compared with the original size, the optimized size comprehensively selected has higher energy absorption, protection and impact resistance effect, and the crushing force is much lower than the original size model and more stable.