The growth of GaN on the LiNbO3 (0001) surface is simulated by means of first‐principles total‐energy calculations. Firstly the adsorption of single N and Ga monolayers is investigated and then the layer‐by‐layer growth of GaN on the polar substrate within different orientations is modeled. While adsorbing a N layer does not heavily affect the substrate morphology, the adsorption of a Ga layer causes a rearrangement of the atomic structure. Furthermore the N layer is more strongly bound to the substrate than the Ga layer. On the basis of our results, we propose a microscopic model for the GaN/LiNbO3 interface. The GaN and LiNbO3 (0001) planes are parallel, but rotated by 30° each other, with in‐plane epitaxial relationship [10$ \bar 1 \bar 2 $0]. In this way the (0001) calculated in‐plane lattice mismatch between GaN and LiNbO3 is minimal and equal to 6.79% of the GaN lattice constant. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)