Graphene‐skinned fiber fabric is prepared by chemical vapor deposition (CVD) of continuous graphene on fabric, which enables conformal graphene coverage on fibers and inherits high electrical and thermal conductivity of graphene. However, in the fabric‐shaped configuration, high electrical and thermal contact resistances between fibers, and the lack of conductive and thermal pathways along radial direction of fibers limit the improvement of electrical and thermal conductivity. Herein, carbon nanotubes (CNTs), due to the 1D structure with excellent electrical and thermal conductivity, are introduced to build rich “bridges” to connect the isolated fibers to build new electron and phonon transport channels. Thus, the conceptual design of CNT/graphene‐skinned glass fiber fabric (CNT/GGFF) is creatively proposed and realized by a carefully designed CVD. Constructing the 3D electrically and thermally conductive network in CNT/GGFF leads to >90% decrease of sheet resistance, 4.5 times increase of tensile strength, and >70% decrease of thermal resistance compared with GGFF, making it promising for applications in composite materials, heat dissipation, and de‐icing. Moreover, the thermal resistance of CNT/GGFF exhibits temperature‐independent, extending applications to aviation and space because changes in thermal conductivity of traditional materials with environmental temperatures can adversely affect the thermal stability, reliability, and lifetime of aircrafts.