•BaFe1/2Sn1/2O3-δ was obtained using the sol-gel method and additional O2 treatment.•Oxygen treatment increases Fe4+ content from 27% to 36%.•The absorption band is strongly broadened and shifted to the visible and IR regions.•Oxygen treatment results in significant increase of conductivity.•BaFe1/2Sn1/2O3-δ exhibits giant dielectric response in a wide frequency range. Barium ferrostannate BaFe1/2Sn1/2O3-δ was obtained using the sol-gel precursor method and additional annealing in O2. Phase purity of ceramics was confirmed by x-ray diffraction, the microstructure and microanalysis of grains were investigated by scanning electron microscopy methods, whereas the valence states and coordination of tin and iron ions were determined using Mössbauer spectroscopy. We found out that as-sintered and O2-treated samples contain 27% and 36% of six-coordinated Fe4+ ions, respectively, whereas Fe3+ ions are five-coordinated. Oxygen treatment results in a decrease of the average sizes of coherent scattering regions, increase of the local distortion of SnO6 octahedra, and significant increase of conductivity. Experiments on diffuse reflection show that the characteristic absorption band is strongly broadened and shifted to the visible and IR regions, which is explained by the formation of a large number of local donor levels in the band gap. Thus, the optical band gap is reduced by Fe-doping as compared to BaSnO3 and can be additionally adjusted by annealing in oxygen. Both as-sintered and O2-treated BaFe1/2Sn1/2O3-δ ceramics exhibit giant dielectric response in a wide frequency range.