Engineering transition-metal-based bifunctional oxygen electrocatalysts with high activity and stability has always been a problem. Traditional bare transition-metal-based nanoparticles supported on the outer surface of carbon materials are susceptible to the Ostwald-ripening effect in a catalytic process, consequently suffering from poor long-term operation. However, constructing a highly efficient and stable bifunctional oxygen electrocatalyst is still challenging. Here, we report graphene-like carbon nanosheets modified with carbon shell-coated binary Co-Ni oxide-based nanoparticles (CoNiOx@C/G-NSs) by one-step pyrolysis method, in which the hybrids show a three-dimensional fluffy and hierarchical porous nanostructure and large numbers of carbon shell-coated binary Co-Ni oxide-based nanoparticles (CoNiOx@C) dispersed on graphene-like carbon nanosheets evenly. More excitingly, the carbon nanosheets are nitrogen-doped. When applied for oxygen evolution reaction (OER) and oxygen reduction reaction (ORR), the onset potential (E-onset) of OER reached 1.26 V, and onset potential of ORR and half-wave potential (E-1/2) reached 0.90 and 0.78 V, respectively. The hybrids showed enhanced methanol tolerance, with few changes in the ORR performance with or without adding methanol, and high stability, with 84% activity retention after 10 h continuous reaction. The productivity of H2O2 is about 5% and the number of electron transfer (n) is about 3.9 in the process of catalyzing ORR; density functional theory calculation reveals its high selectivity in the 4e(-) pathway. Its excellent performance is mainly attributed to the synergistic enhancement effect: three-dimensional fluffy and hierarchical porous nanostructure provided a large catalytic activity area, which enabled the effective participation of species and facilitated rapid mass transfer; the rapid adsorption of O-2 by N-doped graphene-like carbon nanosheets ensured fast electron transport; synergistic reactivity between carbon shell and CoNiOx enhanced the activity, and numerous CoNiOx@C nanoparticles reconciled the electron density of the carbon shell, which introduced more active sites; and the carbon shell weakened the Ostwald-ripening effect and ensured the stability of the nanoparticle. All advantages synergistically enhance the catalytic efficiency and make it one of the best bifunctional oxygen electrocatalysts.