Because high-index facets (HIFs) possess high surface energy, the metal nanoparticles enclosed with HIFs are eliminated during their growth in a conventional shape-controlled synthesis due to the thermodynamics that drives the particles minimizing their total surface energy. This study develops a double-step potential method to prepare an unprecedentedly stellated Au nanocrystals (NCs) bounded by high-index {711} and {331} facets in deep eutectic solvent (DES) medium. The formation of Au NCs bounded by HIFs was systematically studied. It has demonstrated that the shapes of Au NCs are strongly dependent on the size of seeds and the growth potentials as well as the urea adsorbates in the DES. By adjusting the size of seeds and the growth potentials, the stellated Au NCs can be transformed into concave hexoctahedra (HOH) with high-index {421} facets and concave trisoctahedra (TOH) with high-index {991} facets. The electrocatalytic activities of the as-prepared Au NCs are evaluated by glucose oxidation. Thanks to HIFs having high density of atomic steps and kinks) the stellated, TOH, and HOH Au NCs exhibit higher electrocatalytic activity than that of the polycrystalline Au electrode, demonstrating that the steps and kinks serve as the active sites and play an important role in glucose electro-oxidation.