A lithium-ion cell comprising: (A) a cathode comprising graphene as the cathode active material having a surface area to capture and store lithium thereon and wherein said graphene cathode is meso-porous having a specific surface area greater than 100 m2/g; (B) an anode comprising an anode active material for inserting and extracting lithium, wherein the anode active material is mixed with a conductive additive and/or a resin binder to form a porous electrode structure, or coated onto a current collector in a coating or thin film form; (C) a porous separator disposed between the anode and the cathode; (D) a lithium-containing electrolyte in physical contact with the two electrodes; and (E) a lithium source disposed in at least one of the two electrodes when the cell is made. This new Li-ion cell exhibits an unprecedentedly high energy density.