Composites of LDPE filled with different amounts of graphene nanoplatelets (GnP) were prepared in form of films by means of precoating technique and single screw melt-extrusion using two types of screws, compression and mixing. This manufacturing process imposes strong anisotropy on the sample's morphology, in which the nanoplatelets become oriented along the extrusion direction. Such orientation of GnP in LDPE matrix is confirmed by scanning electron microscopy observations and it yields unique electrical properties. As compared to pure LDPE, significant reductions of the through-plane conductivity are found for the composites at relatively low electric fields (<20 kV/mm) at low filler concentrations. Above the field level of 20 kV/mm, a crossover effect is observed that results in a strong field dependency of the conductivity where the non-linear behavior starts to dominate. Moreover, differential scanning calorimetry (DSC) results indicate a decrease in polymer crystallinity of the composite matrix with increasing filler content, whereas thermogravimetric (TG) analysis shows a slight increase in the material's thermal stability. Application of GnP also leads to improvement of mechanical properties, manifested by the increase of Young's modulus and tensile strength in both types of samples.