The ionic conductivities of new perovskite-structured lithium–strontium–aluminum/gallium–tantalum oxides were investigated. Solid solutions of the new perovskite oxides, (LixSr1−x)(Al(1−x)/2Ta(1+x)/2)O3 and (LixSr1−x)(Ga(1−x)/2Ta(1+x)/2)O3, were synthesized using a ball-milled-assisted solid-state method. The partial substitution of the smaller Ga+3 for Ta+5 resulted in new compositions, the structures of which were determined by neutron diffraction measurements using a cubic perovskite structural model with the Pm−3m space group. Vacancies were introduced into the Sr(Li) sites by the formation of solid solutions with compositions (LixSr1−x−y☐y)(Ga[(1−x)/2]−yTa[(1+x)/2]+y)O3, where the composition range of 0≤y≤0.20 was examined for x=0.2 and 0.25. The highest conductivity, 1.85×10−3 S cm−1 at 250 °C, was obtained for (Li0.25Sr0.625☐0.125)(Ga0.25Ta0.75)O3 (x=0.25, y=0.125). Enhanced ionic conductivities were achieved by the introduction of vacancies at the A-sites.