Preparing economic, stable, and highly efficient non-precious-metal materials for the oxygen reduction reaction (ORR) and oxygen evolution reaction (OER) is of great significance to the development of storage technologies and energy conversion. In this manuscript, we report a novel Cu based nano-catalyst as an electrode material fabricated by complexation-reduction method. Benefit from the stable of h-NB and the good electrical conductivity of CNT, the tri-functional electrocatalyst BN/Cu/CNT displays enhanced activity towards ORR and with the high current density of 0.95 mA/cm2, which is comparable to that of commercial Pt/C catalyst (cathodic peak current: 1.05 mA/cm2). The BN/Cu/CNT also demonstrates high catalyst activity for the OER. From the rotating disk electrode and rotating ring-disk electrode tests, the number of electrons exchanged during the ORR is revealed to be 3.92, suggesting a 4e− pathway of O2 reduction to H2O. The as prepared catalyst also has good stability and superior methanol tolerance to the commercial Pt/C catalyst in alkaline medium. Thus, it is anticipated that the BN/Cu/CNT catalyst is surely helpful for providing a new space to develop Pt-free catalyst.