Diffusion of Li⁺ ionsin solidsisa basic principle behindthe operationof Li-ion batteries. Suchdiffusive behavior is represented by the diffusion equation (Fick's law), J = -D × δφ/δx, where J is the diffusion flux, D is the self diffusion coeffcient, φ is the concentration, and x is the position. Although D of Li⁺ ions(DLi)in solids is usually evaluatedby ⁷Li-NMR, diffculties arise for materials that contain magnetic ions. This is because the magnetic ions contribute additional spin-lattice relaxation processes thatis considerably larger than the 1/T₁ expected from only Li diffusion[1,2,3]. This implies that ⁷Li-NMR providesa rough estimateof D_Li for the positive electrode materials of Li-ion batteries, which include transition metal ions in order to compensate charge neutrality during a Li⁺ intercala-tion/deintercalation reaction. This is an unsatisfactory situation since D_Li is one of the primary parameters that govern the charge/discharge rate of a Li-ion battery. We have, therefore, attempted to measure D_Li for lithium-transition-metal-oxides with muon-spin relaxation (μ⁺SR) since 2005 [4,5,6]. Muons do not feel fluctuating magnetic moments at high T, but instead sense the change in nuclear dipole field due to Li diffusion. Even if magnetic moments still affect the muon-spin depolarization rate, such aneffectis, in principle, distinguishable from that of nucleardipole fields. In particular, a weak longitudinal field can be applied that decouples the magnetic and nuclear dipole interactions [7,8]. Here, we wish to summarize our μ⁺SR study on the lithium-transition-metal-oxides, Li_xCoO₂, LiNiO₂, and LiCrO₂.