Efficient removal of heat has become one of the most critical challenges in the development of modern microelectronic devices. However, it is hard to dramatically improve thermal conductivity of composite materials even with highly loaded thermally conductive fillers due to the lack of efficient heat transfer paths. In this article, both horizontal and vertical graphene film/epoxy (GF/E) composites were designed and fabricated and their thermal and mechanical properties were studied. Vertically aligned structure constructed of continuous graphene films forms channels for heat removal. The thermal conductivity of vertical GF/E composites reaches 384.9 W m(-1) K-1 at 44 vol% graphene, i.e. a dramatic enhancement of 3570% per vol% compared to the pure epoxy, and representing the highest value of all epoxy based composites. The cooling performance of light-emitting diode (LED) package with the application of GF/E composites is enhanced by reducing the temperature of LED lamp about 20.7 degrees C compared with the application of pure epoxy. The vertical GF/E composite proved to be a potential material for heat management of LED or other electronic devices. (C) 2017 Elsevier Ltd. All rights reserved.