In this study, current-density vs electric-field intensity characteristics of polypropylene-based nanocomposite films are presented with concentrations of 0%, 2% and 6% nanosize natural clay by weight. Each nanocomposite sample is subjected to a 60-Hz, sinusoidal voltage waveform. During the experiments, applied rms voltage and current are recorded as the voltage increases across the test sample. The test was repeated with five samples with the same nanofiller content. The current-density vs electric-field intensity characteristics indicate a nonlinear behavior for each sample under consideration with some degree of saturation. From these characteristics, it was observed that the inception of saturation occurred at higher electric field intensities for the nanocomposites filled with natural clay than the unfilled polypropylene. The relative permittivity of of each sample was almost constant up to a critical electric field at which the saturation starts. Above that critical electric field, relative permittivity dramatically dropped.