By means of a positive muon spin rotation and relaxation (mu+SR) technique, we have investigate Li and Na ion diffusion in many battery materials. Among them, it was found that Li ions start to diffuse above 200 K in LiFePO4. In order to confirm the Li diffusion in this material, we want to measure the negative muon spin rotation and relaxation (mu-SR) spectrum for LiFePO4. This is because about 35% of the implanted negative muons are captured by oxygen and the captured muon spin sees a local nuclear magnetic field formed by Li and P from a fixed viewpoint. Such experiment provides a clear insight for ion diffusion in solids.