The authors report micro-Raman investigation of changes in the single and bilayer graphene crystal lattice induced by the low and medium energy electron-beam irradiation (5 and 20 keV). It was found that the radiation exposures results in appearance of the strong disorder D band around 1345 1/cm indicating damage to the lattice. The D and G peak evolution with the increasing radiation dose follows the amorphization trajectory, which suggests graphenes transformation to the nanocrystalline, and then to amorphous form. The results have important implications for graphene characterization and device fabrication, which rely on the electron microscopy and focused ion beam processing.