Polymer composites with carbon nanofillers have been regarded as a promising candidate for electronic package materials. The challenge for such materials is to increase the electrical and thermal conductivity of the composites. Herein, we reported an epoxy composite film with high thermal and electrical conductivity that were prepared by loading high volume fraction of well-dispersed multi-walled carbon nanotubes (MWCNTs, around 50 nm in diameter, 1-10 µm in length) and copper nanowires (Cu NWs, 60-70 nm in diameter, 1-5 µm in length) in epoxy matrix. The MWCNT-Cu NW hybrid mats were prepared by a vacuum filtration method with an optimum Cu NW content of 50 wt%. The hybrid mats was then impregnated by epoxy solution to prepare epoxy composite films. The epoxy was modified by the toughening agent to make the composite films tough and flexible. The loading fraction of MWCNTs and Cu NWs was tuned by controlling the viscosity of epoxy solution. A remarkable synergetic effect between the MWCNTs and Cu NWs in improving the electrical and thermal conductivity of epoxy composites was demonstrated. The results showed that the electrical conductivity of nanocomposites with 42.5 wt% epoxy was 1500 S/m, and the thermal conductivity was 2.83 W/m K, which was 10.1 times of the neat epoxy. Its thermal resistance was as low as 1% of the pure epoxy. And the mechanical properties of composites were also investigated. These robust and flexible nanocomposites showed prospective applications as thermal interface materials (TIMs) in the electronic industry.