Binder-free and bifunctional electrocatalysts have vital roles in the development of high-performance metal–air batteries. Herein, we synthesized a vanadium oxide (VO₂) nanostructure as a novel binder-free and bifunctional electrocatalyst for a rechargeable aqueous sodium–air (Na–air) battery. VO₂ nanostructures were grown on reduced graphene oxide coated on carbon paper, which had a carambola morphology. We confirmed the bifunctional nature of VO₂ nanostructures by analyzing their electrocatalytic activity associated with the oxygen reduction reaction and oxygen evolution reaction. The reaction pathway associated with electrocatalytic activity was also affirmed by computational modeling and simulation studies. Thereafter, an aqueous Na–air cell was built using novel binder-free VO₂ nanostructures as the air electrode. The fabricated cell displayed a 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.