Nanodiamond-graphene core-shell materials have several unique properties compared with purely sp(2) -bonded nanocarbons and perform remarkably well as metal-free catalysts. In this work, we report that palladium nanoparticles supported on nanodiamond-graphene core-shell materials (Pd/ND@G) exhibit superior catalytic activity in CO oxidation compared to Pd NPs supported on an sp(2) -bonded onion-like carbon (Pd/OLC) material. Characterization revealed that the Pd NPs in Pd/ND@G have a special morphology with reduced crystallinity and are more stable towards sintering at high temperature than the Pd NPs in Pd/OLC. The electronic structure of Pd is changed in Pd/ND@G, resulting in weak CO chemisorption on the Pd NPs. Our work indicates that strong metal-support interactions can be achieved on a non-reducible support, as exemplified for nanocarbon, by carefully tuning the surface structure of the support, thus providing a good example for designing a high-performance nanostructured catalyst.