We present an experimental investigation on graphene for electrochemical hydrogen storage when employed in a modified reversible polymer electrolyte membrane (MRPEM) fuel cell. Synthesis of graphene nanomaterial is performed to obtain graphene oxide (GO) using the modified Hummers method. Oxides in GO are reduced to get reduced graphene oxide (rGO) using Cedrus deodara (CD) tree's leaf extract. Physical characterisation of the prepared GO and CD-rGO is done to ascertain their properties, viz, internal pore surface area, average pore diameter, etc. Solid electrodes are fabricated from the prepared powdered samples of GO and CD-rGO, and later tested in an MRPEM fuel cell. Electrochemical hydrogen storage capacity of GO and CD-rGO is found to be 1.21 and 2.7 wt%, respectively. It is successfully demonstrated that hydrogen ions could be stored in a porous graphene electrode and recovered back. The obtained results are analysed to draw a relation between physical characteristics of graphene and electrochemical hydrogen adsorption. It is found that higher internal pore surface area attracts more hydrogen storage in ionic form. This research work is a maiden attempt to show, experimentally, the physical/chemical adsorption of hydrogen in graphene when employed in a reversible PEM fuel cell. This surely could contribute towards the development of a safe and efficient alternate powering source with many potential applications.