In this work, we have developed a novel nanocomposite material of ceria (CeO2)-reduced graphene oxide (RGO) by sonochemical route for application as symmetric supercapacitors. CeO2 nanoparticles have been anchored on RGO sheets in order to maximize the specific capacitances of these materials. Nanostructure studies and electrochemical performances of the CeO2 nanoparticles on the RGO sheets were systematically investigated. The morphology and crystalline structure of nanocomposites were examined by field emission scanning electron microscopy (FE-SEM), Fourier transform infrared (FT-IR), and X-ray diffraction (XRD). Electrochemical properties of the nanocomposite electrodes were examined by cyclic voltammetry (CV), galvanostatic charge/discharge and electrochemical impedance spectroscopy (EIS) measurements. CeO2-RGO nanocomposite electrodes exhibited excellent supercapacitive behavior with high specific capacitance of (211 F g-1 at 2 mV s-1 and 185 F g-1 at 2.0 A g-1), high rate capability and well reversibility. Cycling stability of electrode was measured by continues cyclic voltammetry (CCV) technique. Upon 4000 cycles, the specific capacitance of the electrode increases and reaches a maximum value of 105.6 % of the initial value.