Double perovskite oxides A(2)BB'O-6 combining 3d and 4d or 5d transition metal ions at the B and B' sites feature a variety of magnetic and magneto-electric properties. Targeting Ba2FeOsO6, we synthesized powder samples of nonstoichiometric Ba2Fe1.12Os0.88O6 by solid-state reaction from the oxides. The crystal structure was investigated by using synchrotron powder Xray and powder neutron diffraction. In contrast to Ca2FeOsO6 and Sr2FeOsO6, the compound adopts the hexagonal 6L perovskite structure (space group P (3) over bar m1) with partial Fe-Os order at both the face-sharing B2O9 dimer and the corner sharing BO6 transition metal sites. Magnetization, neutron diffraction, and Fe-57 Mossbauer spectroscopy results show that Ba2Fe1.12Os0.88O6 develops ferrimagnetic order well above room temperature at T-C approximate to 370 K. The nonsaturated magnetization curve at 2 K features a magnetic moment of 0.4 mu(B) per formula unit at 7 T and a pronounced hysteresis with a coercive field of about 2 T. Large exchange bias effects are observed when the magnetization curves are measured after field cooling. The peculiar magnetic properties of Ba2Fe1.12Os0.88O6 are attributed to an inhomogeneous magnetic state formed as a consequence of the atomic disorder. Our results indicate that hexagonal double-perovskite-related oxides are a promising class of compounds for finding new materials with potential applications as hard magnets or in the area of spintronics.