Binder free and bi–functional electrocatalyst plays a vital role in the development of high performance metal–air batteries. Herein, we have synthesized a vanadium oxide (VO2) nanostructure as a novel binder free and bi–functional electrocatalyst for rechargeable aqueous sodium–air (Na–air) battery. VO2 nanostructures have been grown on reduced graphene oxide coated on carbon paper which have carambola morphology. We have confirmed bi–functional nature of VO2 nanostructure by analyzing its electrocatalytic activity associated with oxygen reduction reaction (ORR) and oxygen evolution reaction (OER). The reaction pathway associated with electrocatalytic activity was also affirmed by computational modeling & simulation studies. Thereafter, aqueous Na–air cell has been built using novel binder free VO2 nanostructures as air electrode. The fabricated cell displays 0.64 V overpotential gap, 104 mW g–1 power density at 80 mA g–1 current density, 81% round trip efficiency and good cyclic stability up to 50 cycles, which are comparable to the previous best known Na-air batteries.