The curvature dependence of the physisorptions of $H_2$ on graphene surface and their barrier to the chemisorptions has been studied. The graphene with steeper curvature can adsorb $H_2$ stronger due to the more $sp^3$ character of the carbon. However, for the negative curvature, the binding strength of the physisorption and the barrier to the chemisorptions are determined by steric repulsion as well as the $sp^3$ character.