Single-crystal grains of the new oxide LiBa₂AlO₄ were obtained from a sample that had been partially melted by heating a compact of a binary oxide powder mixture having a Li:Ba:Al molar ratio of 4:5:1 ​at 1173 ​K. Single-crystal X-ray diffraction analysis demonstrated that this oxide had a trigonal superstructure (hexagonal lattice with a ​= ​5.7879(2) Å and c ​= ​13.2456(6) Å, space group P3₁21) formed by an ordered Li and Al arrangement. The c-axis period in this structure was found to be approximately twice as long as that in BaZnO₂, the space group of which is also P3₁21, and a three-dimensional framework constructed by sharing all vertices of Li- and Al-centered oxygen tetrahedra. This structure can be derived from the perovskite (ABO₃)-type structure via the orderly replacement of BO₆ octahedra with LiO₄ and AlO₄ tetrahedra. Polycrystalline samples of LiBa₂AlO₄ were synthesized by heating compacts having stoichiometric compositions at 1173 ​K. The relative dielectric constant and dielectric loss values observed for a polycrystalline sample at room temperature were 8.3 and 0.004, respectively. The second harmonic generation intensities for LiBa₂AlO₄ and BaZnO₂ were found to be 4.4 and 19.4 times greater than the value for quartz, respectively.