Reaching the maximum Li storage capacity in Li-ion batteries (LIBs) has been impractical because it requires the use of Li metal itself as the anode. Problematically, Li metal forms dendrites and related unstable structures during battery operation. This results in low coulombic efficiency and cycle life and poses serious safety concerns as the dendrites can cause short circuits. The approaches reported to date either limited Li storage capacity per unit electrode area and cycle life, or they restricted the current density since dendrite formation is more rapid and severe at higher current density. We report here a seamless graphene-carbon nanotube (GCNT) electrode that is capable of reversibly storing large amounts of Li metal with complete suppression of dendrite formation. The GCNT serves as a host material to insert and form Li as a thin coating over its high surface area (~2600 m² g^-1). With a Li storage capacity up to 4 mAh cm^-2 (823 mAh cm^-3) and 25.3 Ah g^-1_G-CNT, the GCNT stores 6.6 times its weight in Li, 68 times greater than does graphite (372 mAh g^-1_C), 6.6 times greater than does Si (3859 mAh g^-1_Si), and far exceeds other Li storage materials. The capabilities, reversibility, and dendrite-free nature of the GCNT bode well for its use as a model structure for electrodes in secondary batteries.