Ab initio calculations under the framework of density functional theory have been applied to calculate electronic properties in Cu-doped ZnO. Cu atom when doped at cation site produces a significant magnetic moment along with half-metallic behavior. The 3d-orbital electrons of the dopant along with the p-orbital electrons from the neighboring oxygen atomsare the main source of magnetism. A detailed spin-spin interaction study has resolved the anomaly of ferromagnetic and anti-ferromagnetic spin ordering in Cu-doped ZnO system. Two Cu-dopants have been doped at different Zn-sites by varying the dopant distances. The ground state energy for each spin-ordered system has been calculated with the spin-polarized condition. Moreover, it has been shown that the origin of the magnetic ordering in Cu-doped ZnO system is following the indirect exchange of Ruderman-Kittel-Kasuya-Yosida (RKKY) model.