Thermal management materials with excellent electromagnetic interference (EMI) shielding performance have attracted research interest in the field of modern electronic devices. Herein, vertical edge rich graphene (VG) was in-situ grafted on the carbon nanotube (CNT) sponge to create connective 3D hybridized carbon skeleton with covalent bonding, then CNT-VG/epoxy composites were constructed to meet the needs of multifunctional application. Impressively, mainly owing to the connectivity of 3D CNT sponge, the conduction ability of interfaces and the defect-rich structure of VG, the obtained CNT-VG/epoxy composites possessed an enhanced EMI shielding effectiveness of 46.9 dB with a thickness of 1 mm and an improved thermal conductivity of 2.23 W m−1 K−1 which contributes to superior thermal management capability. In addition, the excellent structural design also increases the flexural strength by 349.39% compared to pure epoxy resin, achieving a flexural strength of 275.32 MPa and a work of fracture of 9956.98 kJ m−3. The novel multifunctional CNT-VG/epoxy composites with enhanced mechanical property show a bright application prospect in next-generation electronic devices.