A 1-D monohybrid of multiwalled carbon nanotubes and graphene sheets, graphene wrapped multiwalled carbon nanotubes (gC) structure, synthesized in a template-free simple chemical vapor deposition technique without any chemical functionalization, was employed as efficient anode material for Li ion battery. Graphene nanosheets affixed to the multiwalled carbon nanotubes (MWNTs) surface by van der Waal's attraction gives a wrinkled surface to the final 1-D gC configuration. The protrusions on the surface of the tube enhances the porosity of the system and also acts as defects, enhancing lithium adsorption sites while the inner MWNT core gives high electrical conductivity, resulting enhanced electrochemical performance of 373mAhg−1 at 100mAg−1 current density after 150 cycles.