In this study, we report a novel route via microwave irradiation to synthesize a bio-inspired hierarchical graphene--nanotube--iron three-dimensional nanostructure as an anode material in lithium-ion batteries. The nanostructure comprises vertically aligned carbon nanotubes grown directly on graphene sheets along with shorter branches of carbon nanotubes stemming out from both the graphene sheets and the vertically aligned carbon nanotubes. This bio-inspired hierarchical structure provides a three-dimensional conductive network for efficient charge-transfer and prevents the agglomeration and restacking of the graphene sheets enabling Li-ions to have greater access to the electrode material. In addition, functional iron-oxide nanoparticles decorated within the three-dimensional hierarchical structure provides outstanding lithium storage characteristics, resulting in very high specific capacities. The anode material delivers a reversible capacity of ~1024 mA · h · g(-1) even after prolonged cycling along with a Coulombic efficiency in excess of 99%, which reflects the ability of the hierarchical network to prevent agglomeration of the iron-oxide nanoparticles.