Design of materials to be heat-conductive in a preferred direction is a crucial issue for efficient heat dissipation in systems using stacked devices. Here, we demonstrate a facile route to fabricate polymer composites with directional thermal conduction. Our method is based on control of the orientation of fillers with anisotropic heat conduction. Melt-compression of solution-cast poly(vinylidene fluoride) (PVDF) and graphene nanoflake (GNF) films in an L-shape kinked tube yielded a lightweight polymer composite with the surface normal of GNF preferentially aligned perpendicular to the melt-flow direction, giving rise to a directional thermal conductivity of approximately 10 W/mK at 25 vol % with an anisotropic thermal conduction ratio greater than six. The high directional thermal conduction was attributed to the two-dimensional planar shape of GNFs readily adaptable to the molten polymer flow, compared with highly entangled carbon nanotubes and three-dimensional graphite fillers. Furthermore, our composite with its density of approximately 1.5 g/cm(3) was mechanically stable, and its thermal performance was successfully preserved above 100 °C even after multiple heating and cooling cycles. The results indicate that the methodology using an L-shape kinked tube is a new way to achieve polymer composites with highly anisotropic thermal conduction.