A hexagonal oxynitride (Li0.88_0.12)Nb3.0(O0.13N0.87)4 was synthesized through ammonia nitridation of LiNb3O8. The structural analysis revealed that this oxynitride consists of alternate stacking of octahedral and prismatic layers with different Li/Nb ratios: significant amounts of Li and Nb atoms (Li/Nb = 43/57) coexist in the octahedral layer, while the prismatic site is preferentially occupied by Nb (Li/Nb = 3/97). A metallic behavior was accompanied by an abrupt drop of electrical resistivity at about 3 K. Furthermore, large diamagnetism and specific-heat anomaly were observed below this temperature, suggesting the appearance of superconductivity in the Li-Nb oxynitride.