This invention relates to a single-phase perovskite-based solid electrolyte, a solid oxide fuel cell including the same, and a method of manufacturing the same. The method of the invention includes stirring and pulverizing a mixed oxide including lanthanum oxide (La2O3), strontium carbonate (SrCO3), gallium oxide (Ga2O3) and magnesium oxide (MgO); and obtaining an LSGM powder by subjecting the pulverized mixed oxide to primary calcination at a first temperature and then secondary calcination at a second temperature that is higher than the first temperature.