The method of fabricating composites composed of a glass micro ber matrix and the conductive nano bers is proposed. The nano bers incorporating single-walled carbon nanotubes (SWCNTs) and an organic material are spread over the surface of glass micro bers and in some areas between micro bers are coupled together into a branched network. The contributions of intra- CNT and inter-CNT conduction mechanisms in the composites with different contents of SWCNTs are evaluated from the analysis of their impedance spectra. The crossover between two conduction mechanisms is observed at a content of SWCNTs of about 0.1 wt. %.