This proposal describes a muSR experiment on Li-Ti-oxides to see Li diffusion, because muSR is a powerful technique to detect it in the compounds containing magnetic ions. Indeed, according to our preliminary experiment on the positive electrode material LixCoO2, the diffusion constant of Li ions (DLi) estimated by muSR was found to be in good agreement with the prediction of first-principle calculations, while Li-NMR provided considerably lower DLi probably due to the effect of Co 3d spins on the NMR signal. In order to confirm the reliability of DLi estimated by muSR, we wish here to propose a comparative study for Li-Ti-oxides without d electrons, i.e., Li[Li1/3Ti5/3]O4 spinel and Li2TiO3 layered oxide by means of muSR and Li-NMR. Since the two Ti-oxides work as a negative electrode material, the experiment provides essential information on the future solid-state Li-ion batteries.