To improve the thermal conductivity of epoxy resins without losing the insulation, epoxy/silicon nitride (Si3N4) nanowire composites were produced. β-Si3N4 nanowires were synthesized by the carbothermal reduction and nitridation of a homogeneous mixture of silica (SiO2), carbon, and a small amount of cobalt via the vapor–liquid–solid (VLS) mechanism. The ratio of β to α phase in the product Si3N4 increased with heat-treatment temperature; however, the undesirable SiC also increased. By increasing the nitrogen gas pressure in the heat treatment, the ratio of β- to α-Si3N4 increased without producing SiC. The epoxy composite containing Si3N4 nanowires of 60 vol% showed a high thermal conductivity of 9.2 W m−1 K−1 along the preferred orientation of the nanowires.