Dielectric　polymer　composites　with　high　thermal　conductivity　and　high　electric　breakdown　strength　are　needed　for　high　voltage　devices.　Epoxy　resins　is　an　excellent　electrically　insulating　material,　but　low　thermal　conductivity　limits　its　applications.　This　work　aims　to　effectively　enhance　the　thermal　conductivity　and　keep　the　breakdown　strength　of　composites　as　high　as　possible.　In　this　study,　alpha-alumina　(alpha-Al2O3)　particles　with　an　average　size　of　0.21　mu　m,　and　boron　nitride　nanosheets　(BNNSs)　with　an　average　diameter　of　lpm　and　thickness　of　around　40nm　were　homogeneously　mixed　with　epoxy　resin,　and　a　three-phase　composite　was　thus　obtained.　The　superiority　of　this　method　is　that　three-phase　composites　not　only　show　significantly　increased　thermal　conductivity　but　also　have　higher　breakdown　strength　in　comparison　with　that　of　the　two-phase　alpha-Al2O3/epoxy　composites.　It　is　clear　that　epoxy　with　hybrid　fillers　has　great　promising　for　high　thermal　conductive　insulating　materials　for　the　high　voltage　insulation.