The comprehensive study of the low threshold electron emission from multi-layered graphene-like structures (GLS) has been undertaken. The spectrum of emitted electrons from GLS has been obtained by retarding potential method. The state of the surface has been evaluated using scanning electron microscopy (SEM) and field emission microscopy (FEM). The peculiarities of the structure of experimental samples were analyzed by the methods of Raman spectroscopy and X-ray diffraction. It has been found that the maximum of the energy distribution is displaced 6.1-6.8 eV below the vacuum values. It has been observed that with the growth of the electric field the maximum of the energy distribution shifts to the region of low energies while the energy spectrum broadens up to 0.7-1.2 eV. Studies of the emitting surface by FEM and SEM allowed one to conclude that the surface is sufficiently smooth. The field enhancement factor due to the micro-roughness does not exceed 3-10 times.