By using DMo13 software of first-principle pseudo-potential approach based on the density functional theory, theoretical calculation is done on ZnO nanowires at the condition that N atoms are incorporated at different positions and surfaces passivated and not passivated by H. Structural parameter, doping formation energy and electrical structure are analyzed systematically. The result shows that lattice parameter of ZnO nanowires in the growth orientation of [0 0 0 1] plane changes under the conditions of these two kinds of surfaces. Passivation of H leads to an increase in the bond length of Zn-O and makes it easier for N atoms to gather at the surface when doping. Besides, under the condition of two kinds of surfaces, solid solubility will be higher, electro-conductibility will be stronger and p-typed ZnO nanowires will be formed more easily when doped N atoms are nearer to the surface.