In this work, a nanodiamond-based sp(2)/sp(3) hybrid nanostructure composed of a nanodiamond (ND) core and sp(2) surfaces was fabricated for supporting Cu single atoms as a catalyst for selective hydrogenation of phenylacetylene. Cu supported on ND after annealing at 900 degrees C (Cu/ND-900) showed improved activity in comparison to the catalyst of Cu supported on pristine ND (Cu/PND). Surface analyses reveal that Cu single atoms display a high dispersion and an appearance of Cu-(0)/Cu-(I) surface state when supported on ND-900. Our work indicates a possibility of utilizing hybrid carbon structures with tunable sp(2)/sp(3) ratios for approaching improved-performance catalyst system.