We studied growth kinetic processes of AlN molecules on the Al-polar surface of AlN using ab initio and Monte Carlo simulations. Molecular processes were presented and analyzed during the nucleation, ripening, and coalescence stages. The results show that the nucleus number decreases as temperature rises due to the increasing diffusion of the molecules. By analyzing the growth time dependence of average cluster size, interface-limited Ostwald ripening is found to be the main ripening mechanism when the temperature is lower than 1773 K. As cluster-corner crossing diffusion is limited, the growth is fractal-like extension, and the coalescence is achieved through adhesion of clusters, leading to a generally continuous morphology with some vacancies and closure failures, which is in good agreement with our experimental results. Moreover, coverage/temperature kinetic phase diagrams under different deposition rates are presented (from 0.025 to 0.1 ML/s). Our finding suggests that a temperature higher than 1800 K is crucial for growth of an ideal atomic-scale Al-polar AlN surface.