In this study, a novel technique was investigated for the one-step production of graphene layers on a pencil graphite electrode. To the best of our knowledge, this report is the first to describe the formation of graphene layers on a graphite electrode using cyclic voltammetry in 5.0M nitric acid solution. The oxidation of the pencil graphite electrode occurred at the anode. Next, the formed graphene oxide was reduced to graphene over one cycle. The electrochemical characteristics and behaviors of the produced graphene electrodes were investigated by cyclic voltammetry. Physical and morphological characteristics and differences in the electrodes were determined by Raman, XPS and SEM analysis. The graphene electrodes were used as the positive electrode component of a vanadium redox battery. GPGE (the graphene electrode synthesized over 50 cycles in 5M HNO3) had the best performance as a positive electrode in a vanadium redox battery. Moreover, GPGE exhibited great cyclic performance and excellent cycling stability (more than 200 cycles) in cyclic voltammetry. It has been demonstrated that the presented novel processing route is fast, easy, cheap and environmentally friendly for preparation of graphene electrodes which can be used in energy storage systems, sensors, and optoelectronics.