In contrast to proton (H⁺) conductor materials, hydride ion (H^-) conductors are exceedingly rare in nature. Hydride ions are attractive charge carriers with a strong reducing property comparable to that of Mg, indicating potential high voltage and high energy densities. Recently, pure H^- conduction in new La_2-x-ySr_x+yLiH_1-x+yO_3-y oxyhydrides has been demonstrated in experiments, opening a promising avenue for exploring new battery chemistry based on hydride ions. In this presentation, we will elucidate the H^- diffusion mechanism in the distinctive structures of these new oxyhydrides, using first principles calculations. On the basis of our newly gained understandings of H^- diffusion, we performed first principles computation to further optimize and design the oxyhydrides with enhanced properties. Our study demonstrated first principles computation approach for in-depth understanding of new materials and accelerated materials designing with enhanced properties, and is highly transferable to other materials.