Non-noble metal-based bifunctional electrocatalysts may be a promising new resource for electrocatalytic water-splitting devices. In this work, transition metal (cobalt)-incorporated graphitic carbon nitride was synthesized and fabricated in electrodes for use as bifunctional catalysts. The optimum catalytic activity of this bifunctional material for the hydrogen evolution reaction (HER), which benefitted at a cobalt content of 10.6 wt%, was promoted by the highest surface area and conductivity. The activity achieved a minimum overpotential of ~85 mV at 10 mA/cm2 and a Tafel slope of 44.2 mV/dec in an acidic electrolyte. These values of the HER were close to those of a benchmark catalyst (platinum on carbon paper electrode). Moreover, the kinetics evaluation at the optimum catalyst ensured the catalyst flows (Volmer–Heyrovsky mechanism), indicating that the adsorption step is rate-determining for the HER. The activity for the oxygen evolution reaction (OER) indicated an overpotential of ~530 mV at 10 mAcm−2 and a Tafel slope of 193.3 mV/dec, which were slightly less or nearly the same as those of the benchmark catalyst. Stability tests using long-term potential cycles confirmed the high durability of the catalyst for both HER and OER. Moreover, the optimal bifunctional catalyst achieved a current density of 10 mAcm−2 at a cell voltage of 1.84 V, which was slightly less than that of the benchmark catalyst (1.98 V). Thus, this research reveals that the present bifunctional, non-noble metallic electrocatalyst is adequate for use as a water-splitting technology in acidic media.