Cycle injection schemes are often encountered in underground gas storage, and the involved hysteresis directly impacts storage and extraction efficiency. The geological formation generally has hierarchical features containing multiple-level pore sizes. Nevertheless, we still lack a comprehensive understanding of this phenomenon and the pore-scale mechanism behind the geometry affects saturation hysteresis and its cyclic responses. In this work, by 3D printing technology, we fabricate a hierarchically structured porous media chip with dual permeability and uniform one for comparison. Gas-liquid injection cycles are performed to investigate the impact of hierarchical structure on invasion behavior. The phase morphology shows the preferential invasion in 1st-order structure and the capillary trapping in 2nd-order structure, which are supported by the phase saturation at each level of the hierarchical structure. Furthermore, ganglion motion is suppressed in the hierarchical chip while they are significant in the uniform one. Through analysing local invasion behaviors, the connect-jump invasion mode is identified as the primary reason for this suppression. Then, the hysteresis effect is quantified based on the Land model, revealing a weaker saturation hysteresis effect in the hierarchical structure compared with the uniform structure. Finally, the upward trend of relative permeability with saturation is fitted by the van Genuchten model. The model parameter in the hierarchical structure is higher than that in the uniform structure, which is caused by extra pore space in 2nd-order structure. The findings improve the understanding of the hysteresis effect and can promote optimizing strategies for storage and extraction in underground hydrogen storage (UHS).