This proposal describes a muSR experiment for studying a diffusive nature of Li ions in novel anode material for Li-ion batteries. The target compound, LixY2Ti2O5S2 (LxYTOS, x=0-2) has a Ruddlesden-Popper-type layered perovskite structure, but the 12-coordinate site in the perovskite-like slabs is vacant, was recently found to show a reversible Li-intercalation and deintercalation reaction versus Li metal. Furthermore, electrochemical measurements suggest that Li+ ions diffuse very rapidly in the LxYTOS lattice compared with Li-diffusion in the present electrode materials, such as, LiCoO2, LiFePO4, and Li4TiO12. However, there are no reports on a diffusion coefficient of Li+ ions (DLi) in LxYTOS as a function of x and temperature. Since muSR is an optimal technique to detect intrinsic DLi in solids, the proposed experiment leads to a new insight to develop new electrode materials.