Three-dimensional (3D) assemblies based on carbon nanomaterials still lag behind their individual one-dimensional building blocks in terms of mechanical and electrical properties. Here we demonstrate a simple strategy for the fabrication of an open porous 3D self-organized double-hierarchical carbon nanotube tube structure with properties advantageous to those existing so far. Even though no additional crosslinking exists between the individual nanotubes, a high reinforcement effect in compression and tensile characteristics is achieved by the formation of self-entangled carbon nanotube (CNT) networks in all three dimensions, employing the CNTs in their high tensile properties. Additionally, the tubular structure causes a self-enhancing effect in conductivity when employed in a 3D stretchable conductor, together with a high conductivity at low CNT concentrations. This strategy allows for an easy combination of different kinds of low-dimensional nanomaterials in a tube-shaped 3D structure, enabling the fabrication of multifunctional inorganic-carbon-polymer hybrid 3D materials.