We theoretically investigate the thickness dependence of surface stability and adsorption behavior in n layer GaN grown on AlN(0001) substrate to clarify the self-limiting growth on AlN(0001) surface during MOVPE. Our first-principles calculations demonstrate that stability of GaN layers on AlN(0001) substrate is similar to that of GaN(0001) surface irrespective of GaN film thickness. Furthermore, the adsorption behavior of Ga adatom on n layer GaN on AlN(0001) surfaces are independent of film thickness. These results suggest that self-limiting growth is hardly affected by surface structures and ad-sorption behavior. method [8].