The effect of simultaneous alignment of polyethylene (PE) lamellae and graphene nanoplatelets (GnP) on the thermal conductivity (k) of PE-GnP composites is investigated. Measurements reveal a large increase of 1100% in k of the aligned PE-GnP composite using 10 wt% GnPs relative to unoriented pure PE. The rate of increase of k with applied strain for the pure PE-GnP composite with 10 wt% GnP is found to be almost a factor of two higher than the pure PE sample, pointing to the beneficial effect of GnP alignment on k enhancement. Aligned GnPs are further found to be 3 times as effective in enhancing k as in the randomly oriented configuration. Enhancement in k is correlated with the alignment of PE lamellae and GnPs through wide-angle X-ray scattering and polarized Raman spectroscopy. At the maximum applied strain of 400% and using 10 wt% GnPs, a composite k of 5.9 W mK-1 is achieved. These results demonstrate the great potential of simultaneous alignment effects in achieving high k polymer composites.