The band-gap engineering of doped ZnO nanowires is of the utmost importance for tunable light-emitting-diode (LED) applications. A combined experimental and density-functional theory (DFT) study of ZnO doping by copper (Zn ²⁺ substitution by Cu²⁺) is presented. ZnO:Cu nanowires are epitaxially grown on magnesium-doped p-GaN by electrochemical deposition. The heterojunction is integrated into a LED structure. Efficient charge injection and radiative recombination in the Cu-doped ZnO nanowires are demonstrated. In the devices, the nanowires act as the light emitters. At room temperature, Cu-doped ZnO LEDs exhibit low-threshold emission voltage and electroluminescence emission shifted from the ultraviolet to violet-blue spectral region compared to pure ZnO LEDs. The emission wavelength can be tuned by changing the copper content in the ZnO nanoemitters. The shift is explained by DFT calculations with the appearance of copper d states in the ZnO band-gap and subsequent gap reduction upon doping. The presented data demonstrate the possibility to tune the band-gap of ZnO nanowire emitters by copper doping for nano-LEDs.