Polymer composites based on epoxy resin were prepared. Multiwalled carbon nanotubes synthesized on iron-cobalt catalyst were applied as a filler in a polymer matrix. Chlorine or hydroxyl groups were incorporated on the carbon nanotubes surface via chlorination or chlorination followed by hydroxylation. The effect of functionalized carbon nanotubes on the epoxy resin matrix is discussed in terms of the state of CNTs dispersion in composites as well as electrical properties. For the obtained materials current-voltage characteristics were determined. They had a nonlinear character and were well described by an exponential-type equation. For all the obtained materials the percolation threshold occurred at a concentration of about 1 wt%. At a higher filler concentration >2 wt%, better conductivity was demonstrated by polymer composites with raw carbon nanotubes. At a lower filler concentration <2 wt%, higher values of electrical conductivity were obtained for polymer composites with modified carbon nanotubes.