Electrochemical water splitting is considered a promising way of producing hydrogen and oxygen for various electrochemical energy devices. An efficient single, bi-functional electrocatalyst that can perform hydrogen evolution reactions (HERs) and oxygen evolution reactions (OERs) is highly essential. In this work, Co@NC core-shell nanoparticles were synthesized via a simple, eco-friendly, solid-state synthesis process, using cobalt nitrate and with pyrazole as the N and C source. The morphological analysis of the resulting Co@NC nanoparticles was performed with a scanning and transmission electron microscope, which showed Co nanoparticles as the core and the pyrolysis of pyrazole organic ligand N-doped carbon derived shell structure. The unique Co@NC nanostructures had excellent redox sites for electrocatalysis, wherein the N-doped carbon shell exhibited superior electronic conductivity in the Co@NC catalyst. The resulting Co@NC nanocatalyst showed considerable HER and OER activity in an alkaline medium. The Co@NC catalyst exhibited HERs overpotentials of 243 and 170 mV at 10 mA∙cm−2 on glassy carbon and Ni foam electrodes, respectively, whereas OERs were exhibited overpotentials of 450 and 452 mV at a current density of 10 and 50 mA∙cm−2 on glassy carbon electrode and Ni foam, respectively. Moreover, the Co@NC catalyst also showed admirable durability for OERs in an alkaline medium.