An effective cheap method for graphene nanoparticles (GNP) production with controlled size distribution was developed based on anodic oxidation of condensed exfoliated graphite. As it is shown, under certain condition the GNP could be self-organized into a 3-dimensional structure that could be important for understanding of the GNP interaction with different type of surfaces. Based on this feature, a synthesis method for preparation of composites containing GNP and polychlorotrifluoroethylene (PCTFE) was developed. Raman spectroscopy of GNP and GNP/PCTFE revealed a good crystalline structure of synthesized nanoparticles. Laser correlation spectroscopy and electron microscopy studies show that average size of particles ranges from tens to thousands nanometers and thickness consists ten or more graphene layers. We found that conductivity of GNP is of electronic nature. The real and imaginary parts of complex permittivity in the microwave range and electric conductivity at low frequencies were found to be a nonlinear function of a volume content of GNP in GNP/PCTFE composite. It could be explained by a presence of the percolation threshold equals to 0.5 wt.%. Low percolation threshold of GNP/PCTFE composite as self-organized 3D structure, could be a certificate of high surface energy for the particles strongly interacting with the surrounding media.