Studies of the interaction between hydrogen and graphene have been increasingly required due to the indispensable modulation of the electronic structure of graphene for device applications and the possibility of using graphene as a hydrogen storage material. Here, we report on the behaviour of molecular hydrogen on graphene using the gate voltage-dependent resistance of single-, bi-, and multi-layer graphene sheets as a function of H₂ gas pressure up to 24 bar from 300 K to 345 K. Upon H₂ exposure, the charge neutrality point shifts toward the negative gate voltage region, indicating n-type doping, and distinct Raman signature changes, increases in the interlayer distance of multi-layer graphene, and a decrease in the d-spacing occur, as determined by TEM. These results demonstrate the occurrence of dissociative H₂ adsorption due to the existence of vacancy defects on graphene.