Nanocrystalline Cu doped ZnO (Zn1-xCuxO, x = 0, 0.01, 0.02, 0.03 and 0.04) samples were synthesized by high energy ball milling technique (HEBM). The strain developed during ball milling and incorporation of Cu into the Zn-site in ZnO lattice is depicted as broadening of the full width at half maximum (FWHM) of the XRD. The X-ray diffraction peak-widths (FWHM) increases with increase in Cu-concentration. Furthermore, the mechanical impact and the heat produced during ball milling helps in the formation of aggregates. The size of these aggregates was observed to increase with Cu-concentration. Upon calcination, these aggregated structures form particle, resulting in bigger particles for higher concentration of Cu. The XRD results confirm that up to similar to 3 at% of Cu can be doped in ZnO lattice, beyond which CuO precipitates. The impedance spectroscopy and the ac-conductivity results confirm the improvement in dielectric properties of ZnO by Cu doping. The decrease in magnitude of Z' on increase in temperature confirms the negative temperature coefficient of resistance (NTCR) behaviour of the samples. The ac conductivity of ZnO decreases with Cu doping and follows the correlated barrier hopping (CBH) model in the investigated temperature and frequency range.