 Cobalt/graphitic carbon catalysts were prepared from Co-MOF crystals, which were synthesized by a solvothermal method in a Teflon-lined autoclave. The MOF crystals were calcined for 2 h to produce Co-MOF-derived catalysts. X-ray diffraction and X-ray photoelectron spectroscopy analysis showed that calcination of the Co-MOF at 600 °C favors the formation of Co3O4, while calcination at 700 °C produced a catalyst composes of metallic Co embedded in a carbon matrix. Raman spectra showed the carbon layer on the Co particles has graphitic properties. The Co-MOF calcined at 700 °C was observed to have the highest surface area and catalytic activity for oxygen reduction reaction (ORR) and oxygen evolution reaction (OER), respectively. During charge/discharge cycling of the Co-MOF-derived catalyst (N700), the potentials were changed within 10–50 mV from the initial potential after 250 h. This catalyst showed excellent stability for ORR and OER, which were superior to these kinds of catalysts reported in the literatures, because graphitic carbon layers covered on the cobalt nanoparticles.