In the present work, the conductivity of multi-walled carbon nanotube (MWCNT) and epoxy resin matrix nanocomposites produced under the action of a 100-V/cm external sinusoidal electric field is studied, for five MWCNT concentration values. The results showed that the AC electrical conductivities of the nanocomposite samples exhibited a large increase compared to those of pure epoxy resin samples. The conductivity at 40 Hz increased from ~ 10−9 S/m for the pure resin samples to 10−2–10−3 S/m for materials with 0.30 wt% MWCNT concentration, while a further increase of up to ~ 10−1 S/m was achieved on the samples produced under the effects of a sinusoidal field. This phenomenon was attributed to a spatial alignment of the MWCNT inside the epoxy matrix and/or the bending of close MWCNT due to the electrostatic force, which created efficient electric current conduction paths along the MWCNT. A proposed new method estimated the value of the current percolation threshold, yielding a result of 0.016 wt% for the sample that was not subjected to the electric field, which then decreased by approximately one order of magnitude for the samples subjected to the electric field.