Lithium zinc titanate spinel, Li2ZnTi3O8, has received significant attention as a negative electrode material for lithium-ion batteries (LIBs). However, its reaction mechanism has not been fully clarified yet, particularly for the large voltage hysteresis between discharge and charge curves. We hence closely examined (Li1-xZnx)[Li1/3+x/3Ti5/3-x/3]O4 (LZTO) with 0 < x ≤ 0.5 by measuring its open-circuit voltage (OCV) and recording synchrotron radiation X-ray diffraction (XRD) patterns. Here, LZTO is a solid solution of Li[Li1/3Ti5/3]O4 (x = 0) and Li2ZnTi3O8 (x = 0.5), both of which have a spinel-framework structure. For the x = 0.5 sample, the OCV of the discharge reaction differed from that of the charge reaction, particularly at a capacity above 50 mAh·g-1. This difference was due to the migration of Zn2+ ions from tetrahedral sites to octahedral sites, and the Zn2+ ions moved back to tetrahedral sites during the charge reaction. Despite these drastic movements of Zn2+ ions, the cubic lattice parameter of the spinel was maintained during the whole reaction, i.e., zero strain. Perfect zero strain, which has never been reported for any LIB materials, was achieved with the x = 0.25 sample. The reaction mechanism with x = 0.5 and the contributions of the amount of Zn ions are discussed in detail.