First-principles calculations based on spin density functional theory are performed to study the spin-resolved electronic properties of AlN doped with a Cu concentration of 6.25%-18.75%. The ferromagnetic state is more energetically favorable state than the antiferromagnetic state or the nonmagnetic state. For $Al_{0.9375}Cu_{0.0625}N$, a global magnetic moment of 1.26 mB per supercell, with a localized magnetic moment of 0.75 $m_B$ per Cu atom is found. The magnetic moment is reduced due to an increase in the number of Cu atoms occupying adjacent cation lattice position. For $Al_{0.8125}Cu_{0.1875}N$, the magnetism of the supercell disappears by the interaction of the neighboring Cu atoms. The nonmagnetic to ferromagnetic phase transition is found to occur at this Cu concentration. The range of concentrations that are spin-polarized should be restricted within very narrow.