Ba7Li1.75Mn3.5O15.75 is a new hexagonal perovskite whose crystal structure has elements typical for the layered hexagonal perovskites and quasi-one-dimensional oxides, hence representing a new polytype. It has been synthesized via a solid-state microwave route. The crystal structure was solved using a combination of X-ray and neutron diffraction data, which show that Ba7Li1.75Mn3.5O15.75 crystallizes in a hexagonal unit cell with parameters a = 5.66274(2) Å and c = 16.7467(1) Å (V = 465.063(4) Å(3)), with one formula unit, and can be described as columns of face-shared octahedra occupied by Mn(4+) and Li(+) cations and vacancies along the c axis separated in the ab plane by barium atoms. Every sixth layer, the coordination of Mn(5+) and Li(+) changes to tetrahedral. Additional local ordering of manganese and lithium atoms among cationic sites leading to the formation of a rhombohedral supercell has been observed by scanning transmission electron microscopy.