Graphene composites with metal or ceramics are being widely investigated for applications in electronic and energy devices. In this paper, we report the chemical synthesis of graphene and graphite oxide (GO)/ZnO-Ag composites for application in energy storage devices, viz., supercapacitors (SCs). Results of surface modification and morphological studies carried out using Raman spectroscopy, scanning electron microscopy (SEM), and transmission electron microscopy (TEM) data are discussed. The electrochemical performance of these electrode materials in SCs have been investigated using electrochemical impedance spectroscopy (EIS), cyclic voltammetry (CV), and galvanostatic charge-discharge techniques. Performance of the GO/ZnO-Ag composite has been compared with that of the pure graphene in terms of achievable energy and power density. Results show that opening of the GO sheets with ZnO spacer allows storage of more charge than achievable in pure graphene. Silver acts as a catalyst to enhance electrochemically active sites in the electrode material as well as helps in maintaining reasonable electronic conductivity. This is an important feature for the development of high performance SCs since GO/ZnO-Ag composite is a low-cost reproducible material in comparison to graphene.