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Recent theoretical and experimental evaluations demonstrated that KLi6TaO6 is a good Li-ion conductor. In this study, the energetics and detailed mechanism of Li-ion migration, relevant to the point defects of KLi6TaO6, were analyzed by first-principles calculations. Defect formation energy analysis suggested that it has limited chemical potential conditions for attaining Li-excess conditions through doping (substituting tetravalent elements for Ta). The formation of other native defects, such as Li vacancies, hinders the stabilization of the dopant and compensates for the interstitial Li. When the doping is successful, the interactions between the coexisting dopant and interstitial Li can increase the migration energy barrier of the interstitial Li. This phenomenon limits the factors responsible for achieving high Li-ion conductivity in this material. Based on the results of the investigations on KLi6TaO6, isostructural materials of the form ALi6XO6, with various combinations of constituent elements A and X, were each screened on the basis of high stability and low Li-ion migration energy. Twelve structures of the form (A = K or Rb)Li6XO6 were suggested, of which X was pentavalent. They also exhibited limited chemical potential conditions for achieving Li-excess conditions through doping. Combinations of the suggested isostructural oxides and dopants were identified to reduce the interactions between interstitial Li and dopant. Some isostructural oxides were doped using Sn and were evaluated using first-principles molecular dynamics; their Li-ion conductivities at room temperature were found to be comparable with those of garnet-type Li-ion conductors.