Ions are often diffusing in solids. Among many ions, H+, Li+, Na+, O2-, and F- are known to become mobile at high temperatures in solids and they are used for fuel cells and batteries. Very recently, hydride ions (H-) are found to diffuse in inorganic oxyhydride compounds, i.e. LaSrLiH2O2 and related materials. Macroscopic transport measurements provide the evidence of H- diffusion, but the mechanism of such diffusion is still not clarified. Muon spin relaxation (muSR) has a unique feature for detecting ion-diffusion in solids. In particular, the presence of both H- and O2- ions in the lattice suggests that the implanted muons are stable even at high temperatures, based on the past muSR experiments oh MgH2. Therefore, muSR will provide microscopic information in the target materials through the change in local magnetic environments induced by H- diffusion.