Using the first-principle molecular dynamical calculations, we have studied the adatom self-diffusion mechanisms on fcc Al (001), (011) and (111) surfaces. On each surface, there are several mechanisms, among which there is one favour mechanism with the minimum barrier energy. The atomic exchange mechanism along the [100]direction on the (001) surface, the long bridge hopping mechanism along the [110] direction on the (011) surface,and the bridge hopping mechanism along the [112] direction on the (111) surface are the favour mechanisms. The activation energy profiles for various self-diffusion mechanisms are studied in details.