Supercapacitors also known as electrochemical capacitors, that store energy via either Faradaic or non-Faradaic processes, have recently grown popularity mainly because they complement, and can even replace, conventional energy storage systems in variety of applications. Supercapacitor performance can be improved significantly by developing new nanocomposite electrodes which utilizes both the energy storage processes simultaneously. Here we report, fabrication of the freestanding hybrid electrodes, by incorporating graphene and carbon nanotubes (CNT) in pyrrole monomer via its in-situ polymerization. At the scan rate of 5 mV s-1, the specific capacitance of the polypyrrole-CNT-graphene (PCG) electrode film was 453 F g-1 with ultrahigh energy and power density of 62.96 W h kg-1 and 566.66 W kg-1 respectively, as shown in the Ragone plot. A nanofibrous membrane was electrospun and effectively used as a separator in the supercapacitor. Four supercapacitors were assembled in series to demonstrate the device performance by lighting a 2.2 V LED.