The electronic and geometric structure of alpha -Al2O3 (0001) surface with and without adsorbed Co and Ni atoms has been investigated using the full-potential linearized augmented plane-wave density-functional theory method. It has been found that the truncated alpha -Al2O3 (0001) surface-undergoes a large surface reconstruction from its bulk structure, which is further changed upon the metal atom adsorption. Geometries, energies, and electronic properties of the partially optimized and the truncated undistorted alpha -Al2O3 slabs are compared. Electronic "surface state levels" due to the unsatisfied bonding of the Al atoms at both ends of the slab are identified. Among several geometries, the 3-fold oxygen site has been found to be the only stable adsorption site for both Co and Ni atoms. Several factors determine the metal-support interaction between the Co (or Ni) atom and the alpha -Al2O3 substrate. Among these factors, the "screened ligand field" effects of partially occupied 3d electrons and the further relaxation of the alpha -Al2O3 substrate are shown to have the largest contributions to the adsorption energy.