Remarkable hydrogen evolution reaction (HER) or superior oxygen evolution reaction (OER) catalyst has been applied in water splitting, however, utilizing a bifunctional catalyst for simultaneously generating H-2 and O-2 is still a challenging issue, which is crucial for improving the overall efficiency of water electrolysis. Herein, inspired by the superiority of carbon conductivity, the propitious H atom binding energy of metallic cobalt, and better OER activity of cobalt oxide, we synthesized cobalt-cobalt oxide/N-doped carbon hybrids (CoOx@CN) composed of Co-0, CoO, Co3O4 applied to HER and OER by simple one-pot thermal treatment method. CoOx@CN exhibited a small onset potential of 85 mV, low charge-transfer resistance (41 Omega), and considerable stability for HER. Electrocatalytic experiments further indicated the better performance of CoOx@CN for HER can be attributed to the high conductivity of carbon, the synergistic effect of metallic cobalt and cobalt oxide, the stability of carbon-encapsulated Co nanoparticles, and the introduction of electron-rich nitrogen. In addition, when used as catalysts of OER, the CoOx@CN hybrids required 0.26 V overpotential for a current density of 10 mA cm(-2), which is comparable even superior to many other non-noble metal catalysts. More importantly, an alkaline electrolyzer that approached similar to 20 mA cm(-2) at a voltage of 1.55 V was fabricated by applying CoOx@CN as cathode and anode electrocatalyst, which opened new possibilities for exploring overall water splitting catalysts.