We report first-principles self-consistent calculations of the atomistic structure and local electronic densities of states of the system Nb on alpha-Al2O3 (sapphire). We find that a monolayer of Nb strongly prefers those surface sites on Al2O3(0001) that are occupied by Al in the bulk, and the bonding is very ionic. When eight layers of Nb are simulated in contact with O-terminated Al2O3(0001), the metal shows appreciable interlayer relaxation near the interface. When the Al2O3 is terminated instead by Al, the adjacent Nb lattice is much less distorted. We see significant differences in the local electronic structure between these cases.