Rational design and fabrication of nonprecious metallic multifunctional catalysts with superior performance are crucial for energy-related electrochemical devices. Herein, we report the synthesis and electrochemical properties of a sandwich-like Co@Co3O4 embedded into Fe, N, S co-doped reduced graphene oxide (Co@Co3O4/FeNS-RGO) nanocomposite catalyst. The designed Co@Co3O4/FeNS-RGO catalyst is synthesized by pyrolysis of one-pot solvothermal method-induced nano-zeolitic imidazolate framework (ZIF)/graphene oxide nanocomposite using dimethylsulfoxide as both the solvent and sulfur source. The synthesized catalyst exhibits the outstanding electrocatalytic activity in basic media for oxygen reduction reaction and oxygen evolution reactions, which outperforms the commercial Pt/C and IrO2 catalysts, respectively. In addition, the synthesized catalyst also shows a promising electrocatalytic activity towards hydrogen evolution reaction. The performance of the thus-assembled zinc-battery and the overall water-splitting device reveals that the synthesized Co@Co3O4/FeNS-RGO can be practically applied in energy-related electrochemical devices with great activity and stability.