Abstract: The anion-deficient perovskite 4H-BaMnO2+x has been obtained by a topotactic reduction, with LiH, of the hexagonal perovskite 4H-BaMnO3−x. The crystal structure of 4H-BaMnO2+x was solved using electron diffraction and X-ray powder diffraction and further refined using neutron powder diffraction (S.G. Pnma, a = 10.375(2) Å, b = 9.466(2) Å, c = 11.276(3) Å, at 373 K). The orthorhombic superstructure arises from the ordering of oxygen vacancies within a 4H (chch) stacking of close packed c-type BaO2.5 and h-type BaO1.5 layers. The ordering of the oxygen vacancies transforms the Mn2O9 units of face-sharing MnO6 octahedra into Mn2O7 (two corner-sharing tetrahedra) and Mn2O6 (two edge-sharing tetrahedra) groups. The Mn2O7 and Mn2O6 groups are linked by corner-sharing into a three-dimensional framework. The structures of the BaO2.5 and BaO1.5 layers are different from those observed previously in anion-deficient perovskites providing a new type of order pattern of oxygen atoms and vacancies in close packed structures. Magnetization measurements and neutron diffraction data reveal 4H-BaMnO2+x adopts an antiferromagnetically ordered state below TN ≈ 350 K.