We report the observation of room temperature ferromagnetism (FM) in Cu-doped ZnO (ZnO: Cu) thin films synthesized by sol-gel technique. While donor Al(3+) cations are introduced into the ZnO: Cu films, the saturation magnetization decreases rapidly. Cu 2p core-level X-ray photoelectronic spectra demonstrate that the FM is strongly correlated with Cu(2+) cations (3d (9) configuration). To further study the relationship between the FM and acceptors, Na(+) cations are also introduced into the ZnO: Cu films to increase the saturation magnetization. The enhanced FM in the (Cu, Na)-codoped ZnO is suggested to be due to the hybridization between delocalized holes and spin-split Cu 3d states.