Nowadays although the study of In-N co-doping effect on the photoelectric function of ZnO is relatively common, all of the In-N co-doped ZnO are of random doping, and the preferential locality doping using the unpolarized structure of ZnO has not been considered so far. Therefore, in this paper, based on the density functional theory using first-principles plane-wave ultrasoft pseudopotential method, the un-doped and the In-N heavily co-doped Zn1-xInxO1-yNy (x= 0.0625, y=0.125) in different orientations have been set up, and band structures and density of states have been calculated respectively. The calculated results show that the In-N atoms along the c-axis orientation has the advantages of high stability over those in the vertical c-axis direction, the band gap is narrower, the effective mass is smaller, the mobility is greater, and the hole concentration is higher, so that the conductivity of ZnO is higher in the In-N heavily co-doped materials. We believe that these results may be helpful to the design and preparation of the conductivity of In-N heavily co-doped ZnO.