We report on the high-pressure synthesis, crystal structure, and magnetic properties of four novel transition-metal oxyhydrides─Ba2NaVO3H3, Ba2NaVO2.4H3.6, Ba2NaCrO2.2H3.8, and Ba2NaTiO3H3─crystallizing in the double-perovskite structure. Notably, they have a higher hydride content in their anion sites (50%-63%) than known oxyhydrides with perovskite structures do (≤33%). Vanadium and chromium oxyhydrides exhibited Curie-Weiss magnetic susceptibilities with no magnetic ordering down to 2 K, which may be due to geometrical frustration in their face-centered lattices and weak magnetic interactions. Density functional theory calculations revealed that the transition metal-hydride bonding nature of the prepared oxyhydrides is more covalent than that observed for known perovskite oxyhydrides, as evidenced by the shorter bond lengths of the former. Remarkably, our double-perovskite oxyhydrides with a high hydride content may possess a bonding character intermediate between those of known oxyhydrides and hydrides.