Molybdenum atom adsorption and migration behavior on clean graphite (0001) surface have been investigated systematically by using first-principles calculations based on the density functional theory. The Mo atom was not adsorpted at the bridge site of graphite (0001) surface because Mo atom moves towards to the hollow site after geometry optimization. Mo atom has been predicted to adsorb preferentially at the hollow site of graphite (0001) surface because of the larger adsorption energy and the smaller work function. It is found from electronic properties that Mo adsorption on graphite (0001) surface belongs to chemisorptions, which is attributed to the electrons of Mo 4d states transfer to C atoms of graphite (0001) surface. The calculated adsorptive rate suggests that the Mo atom adsorption at the hollow site of graphite (0001) surface is more stable with the increasing of temperature. The optimum energy migration paths for Mo atom diffusion from the hollow site to the nearby hollow site is hollow 1 site -> bridge site -> hollow 2 site by using LST/QST transition state seeking method.