All-solid-state batteries incorporating lithium metal anode have the potential to address the energy density issues of conventional lithium-ion batteries that use flammable organic liquid electrolytes and low-capacity carbonaceous anodes. However, they suffer from high lithium ion transfer resistance, mainly due to the instability of the solid electrolytes against lithium metal, limiting their use in practical cells. Here, we report a complex hydride lithium superionic conductor, 0.7Li(CB9H10)-0.3Li(CB11H12), with excellent stability against lithium metal and a high conductivity of 6.7 × 10-3 S cm-1 at 25 °C. This complex hydride exhibits stable lithium plating/stripping reaction with negligible interfacial resistance (<1 Ω cm2) at 0.2 mA cm-2, enabling all-solid-state lithium-sulfur batteries with high energy density (>2500 Wh kg-1) at a high current density of 5016 mA g-1. The present study opens up an unexplored research area in the field of solid electrolyte materials, contributing to the development of high-energy-density batteries.