We study the oxo-hexametallate Li7TaO6 with first-principles and classical molecular dynamics simulations, obtaining a low activation barrier for diffusion of similar to 0.29 eV and a high ionic conductivity of 5.7 x 10(-4) S cm(-1) at room temperature (300 K). We find evidence for a wide electrochemical stability window from both calculations and experiments, suggesting its viable use as a solid-state electrolyte in next-generation solid-state Li-ion batteries. To assess its applicability in an electrochemical energy storage system, we performed electrochemical impedance spectroscopy measurements on multicrystalline pellets, finding substantial ionic conductivity, if below the values predicted from simulation. We further elucidate the relationship between synthesis conditions and the observed ionic conductivity using X-ray diffraction, inductively coupled plasma optical emission spectrometry, and X-ray photoelectron spectroscopy, and study the effects of Zr and Mo doping.