Molecular dynamics simulation with embedded atom method potentials is performed to study the atomic structure and self-diffusion on three aluminum surfaces: (001), (110) and (111). Using mean-square displacement, structure ordering parameter, radial-distribution function and z-direction density, we find that their atoms on the first layer present obvious self-diffusion then change into liquid-like structure under melting points: Al(110) at 700±10 K, Al(001) at 860±10 K, and Al(111) at 930±10 K. In the liquid-like structure, self-diffusions always take place on the first layer of the original surface along the direction parallel rather than vertical to the surface: some of the diffusions occur on the outermost layer and more diffusions occur outside the original surface. The main diffusion channels of the three surfaces are different: along [001] on Al(110), [110] and [110] on Al(001), and [110], [101] and [011] on Al(111). No inter-layer diffusion takes place in liquid-like structure, which is different from in the liquid structure of melted surface.