Since AlGaN offers new opportunities for the development of the solid state ultraviolet (UV) luminescence, detectors and high-power electronic devices, the growth of AlN buffer substrate is concerned. However, the growth of AlN buffer substrate during MOCVD is regulated by an intricate interplay of gas-phase and surface reactions that are beyond the resolution of experimental techniques, especially the surface growth process. We used density-functional ab initio calculations to analyze the adsorption, decomposition and desorption of group-III and group-V sources on AlN surfaces during MOCVD growth in molecular-scale. For AlCH3 molecule the group-III source, the results indicate that AlCH3 is more easily adsorbed on AlN (0001) than (000overline{1}) surface on the top site. For the group-V source decomposition we found that NH2 molecule is the most favorable adsorption source and adsorbed on the top site. We investigated the adsorption of group-III source on the reconstructed AlN (0001) surface which demonstrates that NH2-rich condition has a repulsion effect to it. Furthermore, the desorption path of group-III and group-V radicals has been proposed. Our study explained the molecular-scale surface reaction mechanism of AlN during MOCVD and established the surface growth model on AlN (0001) surface.