The push for high performing electronic devices with long battery lives has rapidly advanced the field of energy storage systems. Niobium oxides have stood out as promising candidates to improve the storage and rate performance of anodes in lithium- and especially sodium-ion batteries due to their larger interplanar lattice spacing and patulous framework. Herein, we report the first synthesis of a nanosized metal/metal oxide hybrid composite coated by N-doped carbon and anchored onto reduced graphene oxide (NbO/Cu@NC-RGO) through in situ carbonizing of Cu-doped polyoxoniobate precursors. The strong synergistic effects between the uniformly distributed NbO/Cu hybrid nanoparticles, the N-doped carbon coating layer, and graphene substrates not only ensure efficient electron and ion transport, but also boost pseudocapacitive charge storage. The resulting composite exhibits a maximum reversible charge capacity of 580 mA h g-1 after 100 cycles at a current density of 100 mA g-1 when utilized in lithium-ion batteries (LIBs), and 203 mA h g-1 when utilized in sodium-ion batteries (SIBs). For SIBs in particular, a long-lifetime of 1012 cycles is observed when cycled at a high current density of 800 mA g-1. This work represents a promising step forward in the design and preparation of metal oxide composite anodes for LIBs and SIBs.