New anion-deficient hexagonal perovskite-like complex oxides Ba5R2Al2ZrO13 (R = Gd-Lu, Y) and Ba5-ySrySc1.33Al2Zr1.66O13.33 were synthesized and studied by X-ray powder diffraction, electron diffraction, and high-resolution electron microscopy. All the compounds have similar crystal structures based on the 10H close-packed (cchcc)2 stacking of BaO3-x layers. The anion vacancies are located in the h -type lamellae and may occur either in an ordered or in a disordered manner, depending on the R3+ cation type. It is shown that the radius of the rare-earth element critically influences the composition and the possibility of ordering in the crystal structures of these compounds. High resolution electron microscopy revealed the presence of a large number of stacking defects, their number, and size, depending on the type of the rare-earth element. The crystal structures of these compounds can be formally described as intergrowth structures with an alternation of BaZrO3 and β-Ba2ScAlO5-type blocks along the c axis.