Compared with lithium-ion batteries with liquid electrolytes, all-solid-state batteries offer an attractive option owing to their potential in improving the safety and achieving both high power and high energy densities. Despite extensive research efforts, the development of all-solid-state batteries still falls short of expectation largely because of the lack of suitable candidate materials for the electrolyte required for practical applications. Here we report lithium superionic conductors with an exceptionally high conductivity (25 mS cm−1 for Li 9.54 Si 1.74 P 1.44 S 11.7 Cl 0.3 ), as well as high stability ( ∼0 V versus Li metal for Li 9.6 P 3 S 12 ). A fabricated all-solid-state cell based on this lithium conductor is found to have very small internal resistance, especially at 100 ∘C. The cell possesses high specific power that is superior to that of conventional cells with liquid electrolytes. Stable cycling with a high current density of 18 C (charging/discharging in just three minutes; where C is the C-rate) is also demonstrated.