Among the carbon based nanostructured materials, Carbon Nanofibers (CNF) have got unique prominence since past decade due to excellent mechanical and electrical properties combined by their cheap and easy fabrication process. CNF with graphene layered structure were developed by electrospinning of PAN (Polyacrylonitrile) and subsequent post treatments under specialized conditions. The assembly of graphene layers in the form of patches on the CNF surface was examined by Raman spectroscopy and TEM. Structural changes of CNF under different temperatures from 800°C - 1500°C in reducing atmosphere have been investigated. Crystallite size, ID/IG, and FWHM for D and G characteristic bands were evaluated via Raman peak fitting and X-ray diffraction spectroscopy. Results have shown that CNF carbonized at 1500°C with prior external straining (creep stress) applied during the oxidative stabilization process showed emergence of a symmetrical sharp 2D peak in Raman spectrum with I2D/IG ratio of nearly multi-layer graphene. High temperature heat treatment along with creep stress during the stabilization process results in transforming more of the amorphous carbon into the ordered graphitic domains, leading to assembly of graphene layers on carbon nanofiber surface.