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A nanocomposite material, composed of nano-size inorganic-filler added to a low-density polyethylene (LDPE), was subjected to electrical property investigations. The volume resistibility of LDPE, under 80 kV/mm DC field at 90 C, increases by the power of 10 due to the addition of only a few percent of nano-filler. On the other hand, lightning impulse breakdown strength was estimated by using a sphere-plate electrode system not dependent on MgO content in the area of 5 phr or less. From these results, it can be considered that the addition of nano-size inorganic-filler drastically raises the volume resistibility of LDPE without reducing the LDPE's original impulse breakdown strength.