Silver/graphene core/shell nanocomposites were synthesized through a one-step electric explosion of wire method using only silver wires and ethanol. The morphology of the graphene shell structures can be easily formed by alternating the solvent from deionized water to ethanol. Transmission electron microscopy revealed that the size of the prepared silver/graphene core/ shell nanocomposites was in the 10–110 nm range. The Raman spectra showed the formation of graphene shells on silver. A possible formation mechanism of the silver/graphene core/shell nanocomposites is proposed in this study. The crystallinity of the nanoparticles was investigated via X-ray diffraction. The graphene on the surfaces of the nanocomposites containing functional groups was analyzed through Fourier-transform infrared spectroscopy and X-ray photoelectron spectroscopy analyses. Zeta potential and dynamic light scattering analyses were performed to determine the dispersion characteristics of the nanocomposites when redispersed in other solvents.