A template-free strategy has been developed for the controlled synthesis of hierarchically porous gamma-Al2O3 with three dimensional (3D) "cluster-like" architectures assembled from 2D nanosheets (similar to 15 nm thick). This unique structure endows the material with large active surface area, high accessibility and ready mass transport ability, capable of promoting the catalytic performance. As a result, the designed gamma-Al2O3 exhibits high activity for selective oxidation of H2S to elemental sulfur. All the porous gamma-Al2O3 samples show outstanding sulfur selectivity (similar to 100%) below 200 degrees C. At higher temperatures, the H2S conversion increases while the sulfur selectivity decreases. The maximum sulfur yield (93%) can be achieved over the optimal sample at 240 degrees C, which is much higher than those of commercial alumina and most of the reported alumina-based catalysts. The structure-activity relationship of the catalysts has been systematically studied. It is demonstrated that the surface acidity of the gamma-Al2O3 has a great influence on catalytic activity. By means of pyridine and H2S in situ FTIR, the nature of the active sites as well as the reaction mechanism of H2S selective catalytic oxidation over gamma-Al2O3 is revealed, providing important insights into the design of alumina-based materials for the removal of sulfur-containing compounds.