Using high-resolution angle-resolved photoemission spectroscopy, we studied the electronic structure of NaFe${}_{1\ensuremath{-}x}$Cu${}_{x}$As ($x=0.019,0.045,0.14$). With increasing the doping concentration, we found that the Cu dopant introduces extra charge carriers. The overall band dispersions barely change with doping, suggesting that the Cu substitution does not affect local correlations. Similar to the case of NaFe${}_{1\ensuremath{-}x}$Co${}_{x}$As, one electron pocket emerges at the Brillouin zone center at high doping levels. Moreover, the near-E${}_{F}$ spectral weight decreases with increasing the Cu dopant, which explains why the NaFe${}_{1\ensuremath{-}x}$Cu${}_{x}$As shows a poor electronical conductivity at high doping levels.