Zr mono-doped and (Zr,N) co-doped ZnO are investigated by the first-principles calculations. It is found that Zr prefers to substitute Zn site under most growth conditions. The passive (N-Zr-N) complexes create a fully occupied impurity band above the valence-band maximum (VBM) of ZnO, which helps p-type conductivity by reducing the ionization energy, consistent with a new approach to overcome the doping asymmetry [Y.F.Yan, J.B.Li, S.H.Wei, and M.M. Al-Jassim, Phys. Rev. Lett. 98 (2007) 135506]. In comparison with (Ga,N) co-doping, (Zr,N) is found to be probably better dopants to push p-type conductivity in ZnO through the new approach with easier formation of the passive impurity band.