Diffusion of Li+ ions in solids is a basic principle behind the operation of Li-ion batteries. Although a diffusion coefficient of Li + (D Li ) in solids is usually evaluated by 7 Li-NMR, difficulties arise for materials that contain magnetic ions. This is because the magnetic ions contribute additional spinlattice relaxation processes that are considerably larger than the 1/T 1 expected from only Li diffusion. As a result, it is very difficult to estimate correct D Li by Li-NMR, although D Li is one of the primary parameters that govern the charge and discharge rate of a Li-ion battery, particularly for the case of a future solid-state battery. We have, therefore, initiated to measure D Li in solids with muon-spin relaxation (µSR). Here, we summarize our µSR work on Li-diffusion and compare the µSR result with that obtained by QENS from the viewpoint of time window.