We present a systematic study of metal adatom adsorption on graphene by ab initio calculations. The calculations cover alkali metals, sp-simple metals, 3d and group 10 transition metals, noble metals, as well as rare earth metals. The correlation between the adatom adsorption properties and the growth morphology of the metals on graphene is also investigated. We show that the growth morphology is related to the ratio of the metal adsorption energy to its bulk cohesive energy (E(a)/E(c)) and the diffusion barrier (ΔE) of the metal adatom on graphene. Charge transfer, electric dipole and magnetic moments, and graphene lattice distortion induced by metal adsorption would also affect the growth morphologies of the metal islands. We also show that most of the metal nanostructures on graphene would be thermally stable against coarsening.