Lithium (Li) metal solid-state batteries feature high energy density and improved safety and thus are recognized as promising alternatives to traditional Li-ion batteries. In practice, using Li metal anodes remains challenging because of the lack of a superionic solid electrolyte that has good stability against reduction decomposition at the anode side. Here, we propose a new electrolyte design with an antistructure (compared to conventional inorganic structures) to achieve intrinsic thermodynamic stability with a Li metal anode. Li-rich antifluorite solid electrolytes are designed and synthesized, which give a high ionic conductivity of 2.1 × 10-4 S cm-1 at room temperature with three-dimensional fast Li-ion transport pathways and demonstrate high stability in Li-Li symmetric batteries. Reversible full cells with a Li metal anode and LiCoO2 cathode are also presented, showing the potential of Li-rich antifluorites as Li metal-compatible solid electrolytes for high-energy-density solid-state batteries.