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. Display omitted •CMF can be used for loading most of the present cathode materials.•CMF based foldable LIBs cannot be obtained as anode potential lower than 0.9 V.•A potential threshold exists for anode materials to match CMF current collector.•Foldable full LIBs can be prepared if its working voltage avoids dangerous region.