This study reports on the dual-acceptor doping effects on ZnO for obtaining p-type conductivity and effectively tuning the band gap. The electronic and optical properties of undoped, mono-(N, Cu) and dual-(N-Cu) doped ZnO have been investigated using first-principles calculations based on the density functional theory (DFT) in the framework of generalized gradient approximation (GGA). The substitution of N, Cu and N-Cu into ZnO leads to the acceptor levels arise above the valance band insight the p-type conduction nature of ZnO. The electronic and optical properties revealed that the band gap narrowing of ZnO is possible by these elementals doping. However, the heavy dual doping is an effective way leads to create shallower impurity level below Fermi level. Therefore, the dual-doped ZnO can be a potential candidate for stable p-type ZnO for future experiment and optoelectronic devices applications.