Abstract We have developed a model atom for Cu with which we perform statistical equilibrium computations that allow us to compute the line formation of Cu i lines in stellar atmospheres without assuming local thermodynamic equilibrium (LTE). We validate this model atom by reproducing the observed line profiles of the Sun, Procyon and 11 metal-poor stars. Our sample of stars includes both dwarfs and giants. Over a wide range of stellar parameters, we obtain excellent agreement among different Cu i lines. The 11 metal-poor stars have iron abundances in the range − 4.2 ≤ Fe/H ≤ -1.4, the weighted mean of the Cu/Fe ratios is −0.22 dex, with a scatter of −0.15 dex. This is very different from the results from LTE analysis (the difference between NLTE and LTE abundances reaches 1  dex) and in spite of the small size of our sample, it prompts for a revision of the Galactic evolution of Cu.