Catalyst with high catalytic activity and good stability are desirable in the electrocatalytic oxidation of glucose. Herein, Pt concave nanocubes with high-index facets (HIFs) supported by carbon black (Pt CNC/CB) are prepared through a hydrothermal method. The experimental results demonstrate that the peak current densities in different potential regions on the Pt CNC/CB anode are 0.22, 0.20, and 0.60 mA cm−2, respectively. The glucose oxidation reaction shows superior performances in basic and neutral conditions than in acid conditions. Better stability is achieved by Pt CNC/CB than Pt concave nanocubes (Pt CNCs). Abundant surface defects with low-coordinated atom numbers, such as the steps, kinks, and edges, are served as active sites in the electrocatalytic oxidation of glucose. With the addition of carbon black, the catalytic activity can be improved by facilitating the full exposure of the active surface defects on the HIFs of Pt CNCs. Moreover, to address the aggregation of Pt CNCs, caused by the high surface energy of HIFs, the introduction of carbon material is an effective way to preserve the HIFs, and thus enhance the stability of the catalyst. Hence, the prepared Pt CNC/CB electrocatalyst has great potential to be applied in the electrooxidation of glucose.