Polymer matrix composites filled with carbon nanoparticles are promising materials for many applications, but their properties strongly depend on the particle features, concentration and distribution within the matrix. Here we present a study of the electrical resistivity and the low-frequency voltage fluctuation of composites based on epoxy resin filled with onion-like carbon (OLC) of different sizes (40–250 nm) above the percolation threshold, which should clarify the electrical transport characteristics in these materials. Electrical measurements were performed in the temperature range of 78 to 380 K, and voltage noise analysis was carried out from 10 Hz to 20 kHz. At low temperatures (below 250 K), thermally activated tunneling, variable-range hopping and generation–recombination of charge carriers take place. Above 250 K, the rapid expansion of the matrix with the temperature increases the resistivity, but above ~330 K, the conductivity of the matrix becomes significant. Quasi one-dimensional electrical transport is observed in composites with the smallest particles (40 nm), while in composites with the largest particles (220–250 nm), the dimensionality of the electrical transport is higher. The temperature dependence of the electrical conductivity of composites with smaller particles is more sensitive to matrix expansion.