First-principles calculations based on spin density functional theory are performed to study the spin-resolved elec- tronic properties of ZnO codoped with Cu and N. (Cu, N)-codoped ZnO exhibits magnetism, and the total magnetic mo- ment mainly originates from the p--d hybridization of Cu-N and Cu-O as well as p--p coupling interaction between N and O at the Fermi level. The Zn34Cu2035N1 favors energetically a ferromagnetic ground state due to the existence of stable Cu-N-Cu complex. These results imply that the (Cu, N)-codoped ZnO is a promising dilute magnetic semiconductor free of magnetic precipitates, which could broaden the horizon of currently known magnetic systems.