Supported copper has a great potential for replacing the commercial palladium-based catalysts in the field of selective alkynes/alkadienes hydrogenation due to its excellent alkene selectivity and relatively high activity. However, fatally, it has a low catalytic stability owing to the rapid oligomerization of alkenes on the copper surface. In this study, 2.5 wt% Cu catalysts with various Cu:Zn ratios and supported on hierarchically porous alumina (HA) were designed and synthesized by deposition–precipitation with urea. Macropores (with diameters of 1 μm) and mesopores (with diameters of 3.5 nm) were introduced by the hydrolysis of metal alkoxides. After in situ activation at 350 °C, the catalytic stability of Cu was highly enhanced, with a limited effect on the catalytic activity and alkene selectivity. The time needed for losing 10% butadiene conversion for Cu1Zn3/HA was ~40 h, which is 20 times higher than that found for Cu/HA (~2 h), and 160 times higher than that found for Cu/bulky alumina (0.25 h). It was found that this type of enhancement in catalytic stability was mainly due to the rapid mass transportation in hierarchically porous structure (i.e., four times higher than that in bulky commercial alumina) and the well-dispersed copper active site modified by Zn, with identification by STEM–HAADF coupled with EDX. This study offers a universal way to optimize the catalytic stability of selective hydrogenation reactions.