New types of carbon nanomaterials, such as multiwalled carbon nanotube (MWCNT) and graphene nanoplatelet (GNP), have attracted much attention in enhancing the thermal conductivity of polymers. However, due to the high electric conductivity of carbon materials, it is difficult for carbon-based epoxy to achieve the high thermal conductivity while obtaining desired dielectric property. In this article, using GNP and MWCNT modified by titanate coupling agent (PN-105), a novel method for highly thermally conductive, but electrically insulating epoxy nanocomposites is reported. The experimental results show that the 4% modified MWCNTs/epoxy nanocomposite has presented a simple thermal conductivity network, which can significantly improve the thermal conductivity of epoxy resin (EP), about 6.5 times higher than pure epoxy. Co-filled with 2% GNPs and 4% MWCNTs, the thermal conductivity of the epoxy nanocomposite is increased to 2.04 W/mK, 957% higher than pure epoxy. In addition, the dielectric constant of the composite is 9.1, which is maintained within an acceptable range. The dynamic mechanical results show that the filling of carbon materials can reduce the storage modulus and the loss factor of EP.