After purification by Fenton treatment, commercial diamond nanoparticles (NPs) are a suitable solid support for the deposition of Cu nanoparticles. Heating at 500 °C under hydrogen proved to be a convenient annealing process for Fenton-purified diamond NPs that decreased the population of surface carboxylic acid groups and lead to samples with average Cu particle sizes of 3–4 nm. The samples of Cu NPs supported on diamond NPs have been characterized by IR and X-ray photoelectron spectroscopy, as well as XRD and TEM. It was concluded that the samples contained Cu0 as well as CuI and CuII species. The resulting diamond-supported Cu NPs were highly active for the selective aerobic oxidation of aromatic thiols to the corresponding disulfides, whereas aliphatic thiols exhibited much lower reactivity because of some poisoning and catalyst deactivation produced by aliphatic thiols. The Cu catalysts used for thiophenol oxidation could be reused in four consecutive runs with 4 % of decrease in the catalytic activity. This Cu catalyst exhibited similar catalytic activity, but is considerably more affordable, as an analogous diamond-supported Au catalyst.