Positive-and negative-muon spin rotation and relaxation (μ ± SR) was first used to investigate fluctuations of nuclear magnetic fields in an olivine-type battery material, LiMnPO 4 , in order to clarify the diffusive species, namely, to distinguish between a μ + hopping among interstitial sites and Li + ions diffusing in the LiMnPO 4 lattice. Muon diffusion can only occur in μ + SR, because the implanted μ − forms a stable muonic atom at the lattice site, and therefore any change in linewidth measured with μ − SR must be due to Li + diffusion. Since the two measurements exhibit a similar increase in the field fluctuation rate with temperature above 100 K, it is confirmed that Li + ions are in fact diffusing. The diffusion coefficient of Li + at 300 K and its activation energy were estimated to be 1.4(3) × 10 −10 cm 2 /s and 0.19(3) eV, respectively. Such combined μ ± SR measurements are thus shown to be a suitable tool for detecting ion diffusion in solid-state energy materials.