High ionic conductivity solid-state electrolytes are essential for powerful solid-state lithium-ion batteries. With density functional theory and ab initio molecular dynamics simulations, we investigated the crystal structures of Li3YBr6 and Li3LaBr6. The lowest energy configurations with uniform distribution of lithium ions were identified. Both materials have wide electrochemical stability windows (ESW): 2.64 V and 2.57 V, respectively. The experimental ESW for Li3YBr6 is 2.50 V. Through extrapolating various temperature diffusion results, the conductivity of Li3YBr6 was obtained at room temperature, approximately 3.9 mS/cm, which is comparable to the experimental value 3.3 mS/cm. Li3LaBr6 has a higher conductivity, a 100% increase compared with Li3YBr6. The activation energies of Li3YBr6 and Li3LaBr6 through the Arrhenius plot are 0.26 eV and 0.24 eV, respectively, which is also close to the experimental value of 0.30 eV for Li3YBr6. This research explored high ionic conductivity halide materials and will contribute to developing solid-state lithium-ion batteries.