Pure and Cu-doped zinc oxide (ZnO) nanoparticles were prepared using a chemical method. The dopant concentration (Cu/Zn in atomic percentage (wt%)) is varied from 0 to 3 wt%. Structural characterization of the samples performed using X-ray diffraction (XRD) confirmed that all the nanoparticles of zinc oxide are having polycrystalline nature. Morphological studies were conducted using field emission scanning electron microscopy (FESEM) to confirm the grain size and texture. Electrical measurements showed that the AC conductivity initially decreases and then rises with increasing Cu concentration. The UV–Vis studies showed absorbance peaks in the 200–800 nm region. It is found that the absorbance does not significantly change with doping. This fact is further confirmed from the band-gap calculations using the reflectance graphs. When analysed in terms of Burstein–Moss shift, an increase of band gap from 3.42 to 3.54 eV with increasing Cu concentration is observed. In the photoluminescence (PL) studies a red-shift is observed with increasing dopant concentration.