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.