Herein, a novel material with an excellent electrocatalytic activity for the oxygen reduction reaction (ORR), composed of onion-like carbon@Co nanoparticles (NPs) incorporated on defect-rich N-doped graphene nanoribbons (C@Co-NGR), is prepared via a combination of nitric acid etching and subsequent high-temperature treatment of the as-synthesized C@Co-N doped carbon nanotubes. The as-prepared C@Co-NGR exhibits excellent electrocatalytic activity for the ORR in 0.10 M KOH with a half-wave potential of 0.830 V (vs. a reversible hydrogen electrode, RHE), which is 21 mV more positive than that of a commercial 20 wt% Pt/C catalyst. Moreover, it shows a higher stability and better methanol tolerance than the commercial Pt/C catalyst in alkaline solution, with almost no shift in the ORR polarization curve after 3000 cycles and no change of the ORR peak in the cyclic voltammogram in the presence of 1.0 M methanol. Most importantly, the C@Co-NGR also exhibits a comparable activity for the oxygen evolution reaction (OER) in 0.10 M KOH solution, in which the overpotential needed to achieve a current density of 10 mA cm-2 is 410 mV, comparable to that of the state-of-the-art commercial RuO2 catalyst (370 mV, vs. RHE). This makes the C@Co-NGR one of the best non-precious-metal catalyst for OER and ORR in alkaline solution ever reported.