We investigated the effect of oxygen annealing on dielectric properties of LuFeCuO4 mainly by dielectric measurements and transmission electron microscopy experiments. It was found that the leakage current density decreases with high-pressure oxygen annealing and the size of nanodomains with orientational polarization increases, which is characterized by the short-range ordering of Fe3+ and Cu2+ ions on a triangular lattice. In addition, the absolute value of relative permittivity epsilon ' decreases with oxygen annealing and epsilon ' exhibits a broad peak in the temperature window between room temperature and 550 K, which is similar to that observed in relaxor ferroelectric materials. The present experimental results suggest that the number of oxygen vacancics has a crucial effect on dielectric properties of LuFeCuO4. [DOI: 10.1143/JJAP.47.8464]