Intravenous pharmacological dose of ascorbate has been proposed as a potential antitumor therapy; however, its therapeutic efficacy is limited due to the slow autoxidation. Here, we report that palladium (Pd) nanocrystals, which possess intrinsic oxidase-like activity, accelerate the autoxidation of ascorbate, leading to the enhancement of its antitumor efficacy. The oxidase-like activity of Pd nanocrystals was facet-dependent, with the concave nanostructure enclosed by high-index facets catalyzing ascorbate autoxidation more efficiently than the planar nanostructure enclosed by low-index facets. Our first-principles calculations provide the underlying molecular mechanisms for the facet-dependent activation of O2 molecule and subsequent ascorbate oxidation. Further in vitro and in vivo assays demonstrate the enhancement of the antitumor efficacy of ascorbate with these Pd concave nanocubes. Our animal experiments also indicate the combined approach with both ascorbate and Pd concave nanocubes displays an even better efficacy than currently available clinical medicines, with no obvious cytotoxicity to normal cells.