Polymers offer several advantages such as low cost, light weight, corrosion resistance and ease of processing, however, they have much lower intrinsic thermal conductivity (<0.5 W/mK) compared to metals (> 20 W/mK) which hinders their widespread applicability in thermal management technologies. Enhancement in thermal conductivity of polymer materials will lead to their more widespread use in applications such as power electronics, electric motors and heat exchangers. The focus of this research is on the effect of molecular alignment on thermal conductivity enhancement of polyethylene/graphene (PE/GNP) nanoplatelet composite materials. Pure high density polyethylene and PE/GNP nanocomposites with 7 and 10 wt% graphene nanoplatelets are prepared using melt-compounding method. Mechanical stretching is applied to achieve molecular chain alignment and several characterization techniques (Wide Angle X-ray Spectroscopy, Laser Scanning Confocal Microscopy, Scanning Electron Microscopy and Atomic Force Microscopy) are used to investigate the impact of mechanical stretching on PE chains and GNP flakes alignment. Finally, thermal conductivity of specimens is measured using a created set-up based on the Angstrom method. The obtained results demonstrate the promise of alignment effects in achieving high thermal conductivity values.