Local electric-field-induced anodic oxidation is one of the earliest and most extensively studied techniques in biasassisted AFM nanolithography. Except the water bridge created between the tip and the sample surface, local anodic oxidation (LAO) process strongly depends on the tip-sample voltage and especially on the electric field distribution under the tip apex center. Once electric field is formed, its distribution and intensity can be modified by changing the tip-sample voltage and separation. The electric field provides the oxidation kinetics of nanoscale electrochemical reaction and controls the spacial resolution of the fabricated structures. In this paper, the s-wave tip quantum model, the influence of the bias voltage and the electric field strength on oxide structures and the theory of electric-field-induced LAO have been analyzed. In addition, dotarray nanogratings, one-dimensional nanogratings and twodimensional nanogratings are fabricated by using electric-fieldinduced LAO process with AFM in the ambient atmosphere.