We carried out ab initio density functional calculations about elementary reactions, which are constituents of Al-CVD. Calculated rate constants and their temperature dependency were employed to clarify the reaction mechanism. In this work, we studied Al-film growth on an Al(111) surface using DMEAA (dimethyl-ethyl amine alane) as source gas. In the previous work, we have found that DMEAA once get adsorbed to the surface and then only DMEA dissociates from the surface. We therefore concentrated on several elementary reactions on the surface supposed to occur from alane molecules. We attached an alane molecule to a cluster constituted of eighteen Al atoms. The energy diagrams for each elementary reaction were calculated based on the fully optimized structures of reactants, transition states, and products. All calculations were carried out with the density functional theory (DFT) at the level of B3P86/LanL2DZ. Then we obtained the rate constants by the transition state theory with quantum tunneling correction. We have found that the adsorbed alane molecules dissociate to AlH and two hydrogen atoms on the surface, and that H atoms are easily desorbed from the surface as gas-phased hydrogen molecules. We may conclude that Al-films grow by the desorption of H after the cohesion of AlH. The rate constants obtained in this study will be utilized to calculate the film growth rate in kinetic study.