The merits of zinc metal anodes such as high chemical stability, low cost and ultrahigh volumetric capacity endow Zn based batteries/hybrid capacitors with great potential applications for electronic products. However, unstable stripping/plating of zinc anodes tends to cause the formation of protuberances/dendrites and side reactions such as water decomposition on anode surfaces, eventually leading to the failure of Zn based electrochemical energy storage devices. Herein, we report the fabrication of free-standing, highly flexible and conductive carbon nanotube (CNT)/paper scaffolds to stabilize zinc metal anodes. The free-standing CNT scaffolds only need to be placed between zinc anodes and separators when assembling zinc anode-based batteries/hybrid capacitors. On the surface of the zinc electrode, the scaffolds’ porous skeleton mechanically regulates Zn2+ deposition sites and their conductive CNT networks maintain a stable electric field during Zn stripping/plating processes, thus retarding the formation of protuberances/dendrites and the occurrence of side reactions. The scaffold-stabilized zinc anodes displayed small polarization voltages, a long cycling life over 1800 h and superior capability for fast charging-discharging. In addition, benefiting from the high electrochemical stability and reversibility of the scaffold-stabilized zinc anodes, zinc-ion batteries/hybrid capacitors with ultralong cycle lives were successfully constructed. This work provides a scalable approach to stabilize zinc metal anodes for long-life zinc-ion batteries and zinc-ion hybrid capacitors.