In this work, conductive polymer poly(3,4-ethylenedioxythiophene) (PEDOT) was synthesized on the surface of graphene oxide (GO) and reduced graphene oxide (rGO) sheets via in-situ microemulsion polymerization process to achieve graphene oxide-poly(3,4-ethylenedioxythiophene) (GO-PEDOT) and reduced graphene oxide-poly(3,4-ethylenedioxythiophene) (rGO-PEDOT) nanocomposites. Nanofibers of PEDOT, GO-PEDOT, rGO-PEDOT and GO on poly(acrylonitrile-costyrene) (P(AN-co-St)) matrice have also been fabricated due to their high potential in using as electrodes for flexible supercapacitors. As demonstrated by scanning electron microscope, atomic force microscope and spectroscopic techniques, PEDOT has been succesfully synthesized on the surface of the GO and rGO sheets. The SEM results demonstrate that nanofibers have beadless structure with a diameter range less than 300 nm. The electrochemical capacitive properties of the nanofibers were investigated by using electrochemical impedance spectroscopy. The electrochemical measurements reveal that GO enhances capacitive behavior of PEDOT nanofibers more than rGO, but both GO and rGO improve the electrochemical performance of the nanofibers.