Flexible carbon nanotube macro-films (CMFs) are perfect current collectors for preparing foldable lithium-ion batteries (LIBs). However, selecting appropriate anodes for electrode is difficult because of the different potentials (vs. Li/Li+) of carbon nanotubes and traditional metallic current collector. This study demonstrated an additional reaction at potential below 0.9 V (vs. Li/Li+) caused by CMF, And Li+ will be constrained, which decreased capacity of anode/CMF electrode. Conversely, results changed when the anode potential exceeded 0.9 V (vs. Li/Li+) because Li+ passed the potential threshold, and the CMF retained its electrochemical inactivity. Consequently, the CMF-based foldable LIBs performed well. The potential threshold mechanism of anode is expected to provide new impetus to both academia and industry for exploring flexible or foldable LIBs. (C) 2016 Elsevier B.V. All rights reserved.