Vertically oriented carbon structures constructed from low-dimensional carbon materials are ideal frameworks for high-performance thermal interface materials (TIMs). However, improving the interfacial heat-transfer efficiency of vertically oriented carbon structures is a challenging task. Herein, an orthotropic three-dimensional (3D) hybrid carbon network (VSCG) is fabricated by depositing vertically aligned carbon nanotubes (VACNTs) on the surface of a horizontally oriented graphene film (HOGF). The interfacial interaction between the VACNTs and HOGF is then optimized through an annealing strategy. After regulating the orientation structure of the VACNTs and filling the VSCG with polydimethylsiloxane (PDMS), VSCG/PDMS composites with excellent 3D thermal conductive properties are obtained. The highest in-plane and through-plane thermal conductivities of the composites are 113.61 and 24.37 W m-1 K-1, respectively. The high contact area of HOGF and good compressibility of VACNTs imbue the VSCG/PDMS composite with low thermal resistance. In addition, the interfacial heat-transfer efficiency of VSCG/PDMS composite in the TIM performance was improved by 71.3% compared to that of a state-of-the-art thermal pad. This new structural design can potentially realize high-performance TIMs that meet the need for high thermal conductivity and low contact thermal resistance in interfacial heat-transfer processes.