The dispersion of transition metals and alkaline earth metals on prisitine and defective graphenes is studied with the use of first principles calculations. The effect of vacancy on binding properties of metal atoms to the graphene and with hydrogen molecules is particularly investigated. It is found that pure carbon sp²-bonded surfaces are ineffective for holding metal atoms without clustering and thus for hydrogen adsorption. The vacancy defect is shown to enhance the metal binding energy and thus its dispersion and also improve the hydrogen adsorption, particularly for Ca. The hydrogen storage capacity is estimated from the maximal number of hydrogen molecules adsorbed on such metal atoms.