Experimental evidence shows that small Cu2O nanoparticles exhibit ferromagnetic or paramagnetic properties, allowing for the promising possibility to recycle the catalyst Cu2O easily in wastewater treatment. In this paper, theoretical calculation studying the magnetic property of copper/oxide clusters is reported. A series of CumOn ((m, n) = (4, 1); (4, 2); (4, 5); (16, 15); (28, 15); (44, 15); (28, 27)) clusters were investigated using generalized gradient approximation (GGA) and the Hubbard U (GGA+U) method within density functional theory (DFT). It is found that the electronic structures of bulk Cu2O calculated by the GGA and GGA+U are similar. The structures of CumOn ((m, n) = (4, 1); (4, 2); (4, 5)) are all planar. For the bulk-product CumOn ((m, n) = (16, 15); (28, 15); (44, 15); (28, 27)), O atoms prefer to be the outermost atoms. We classified two types of clusters on the basis of their O to Cu atomic ratios. One is O-rich clusters, i.e., Cu4O5, Cu16O15, and Cu28O27. The other is O-poor clusters, i.e., Cu4O, Cu4O2, Cu28O15, and Cu44O15. The calculation results show that the O-rich clusters have longer average Cu-Cu bonds and larger binding energy than those of the O-poor ones. More interestingly, the former are magnetic and give ferromagnetic ordering while the latter are nonmagnetic. The hydrogenation of O-terminated clusters can improve its stability but suppress its magnetism. The study may be extremely useful for the potential applications of Cu2O nanopaticles in the catalysis and semiconductor fields.