Graphene nanosheets (GNSs) were modified with aqueous ammonia and hydrogen peroxide, to obtain amine (–NH2) functionalized GNSs (AFGNSs) and enhance the bondings between the GNSs and epoxy matrix. We report an easy and efficient approach to improve the mechanical properties and thermal conductivity of epoxy matrix composites by combining one dimensional multi-walled carbon nanotubes and two dimensional AFGNSs. The long and tortuous MWCNTs can bridge adjacent AFGNSs and inhibit their aggregation, resulting in an increased contact surface area between GNS/MWCNT structures and the polymer. A remarkable synergetic effect between the GNSs and MWCNTs on the enhanced mechanical properties and thermal conductivity of the epoxy composites was demonstrated. The addition of 2 wt.% MWCNT-GNS hybrid fillers improved the tensile strength and flexural strength of the pristine epoxy by 20.71% and 55.51%, respectively. Thermal conductivity increased by 93.71% using MWCNT-GNS hybrid fillers compared to non-derivatised epoxy. This study has demonstrated that 2-D GNSs and 1-D MWCNTs have an obvious synergetic reinforcing effect on the mechanical properties and a remarkable thermal conductivity enhancement in epoxy composites which provides an easy and effective way to design and improve the properties of composite materials.