A novel lightweight three-dimensional (3D) composite anode for a fast-charging/discharging Li-ion battery (LIB) was fabricated entirely using one-dimensional (1D) nanomaterials, i.e., Cu nanowires (CuNWs) and multi-walled C nanotubes (MWCNTs). Because of the excellent electrical conductivity, high-aspect ratio structures, and large surface areas of these nanomaterials, the CuNW-MWCNT composite (CNMC) with 3D structure provides significant advantages regarding the transport pathways for both electrons and ions. As an advanced binder-free anode, a CuNW-MWCNT composite film with a controllable thickness (~600 μm) exhibited a considerably low sheet resistance, and internal cell resistance. Furthermore, the random CuNW network with 3D structure acting as a rigid framework not only prevented MWCNT shrinkage and expansion due to aggregation and swelling but also minimized the effect of the volume change during the charge/discharge process. Both a half cell and a full cell of LIBs with the CNMC anode exhibited high specific capacities and Coulombic efficiencies, even at a high current. More importantly, we for the first time overcame the limitation of MWCNTs as anode materials for fast-charging/discharging LIBs (both half cells and full cells) by employing CuNWs, and the resulting anode can be applied to flexible LIBs. This innovative anode structure can lead to the development of ultrafast chargeable LIBs for electric vehicles.