This proposal describes a muSR experiment on Li-Mn-oxides to see Li diffusion, because muSR is a powerful technique to detect it in the compounds containing magnetic ions. Indeed, according to our recent 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-principles 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 study for the Li[NiyMn2-y]O4 spinel with a high charge/discharge voltage versus Li (4.7 V). This spinel is thus thought to be a promising candidate for a cathode material, particularly for the solid-state Li-ion batteries.