The　non-centrosymmetric　LiBaB9O15　single　crystal　was　synthesized　by　employing　high-temperature　solution　reaction　methods　at　830　degrees　C.　Single-crystal　X-ray　diffraction　analysis　showed　that　it　crystallized　in　the　non-centrosymmetric　space　group　R3c,　with　cell　dimensions　a　=　10.973(1)　angstrom　,　c　=　17.049(2)　angstrom　,　Z　=　6　and　V　=　1777.8(3)　angstrom(3),　having　3D　frameworks　consisting　of　[B(3)O7](5-)　groups　bridged　by　O　atoms,　with　channels　occupied　by　Li+　and　Ba2+　cations.　The　atomic　positions　taken　from　X-ray　diffraction　data　were　optimized　by　minimizing　the　forces　acting　on　the　atoms.　From　the　relaxed　geometry,　the　electronic　structure　and　the　chemical　bonding　were　determined　and　various　spectroscopic　features　were　calculated　and　compared　with　experimental　data.　The　state-of-the-art　all-electron　full-potential　linearized　augmented　plane　wave　method　within　the　Ceperley-Alder　local　density　approximation　and　the　gradient　approximation　was　used　to　solve　the　Kohn-Sham　density　functional　theory　equations.　Very　good　agreement　between　the　measurements　and　the　calculations　was　found.　The　calculated　effective　mass　ratio　of　heavy　holes　(m*(hh)/m(e)),　light　holes　(m*(lh)　=　m(e))　and　(m*(lh)/m(e))　electrons　was　0.4670,　0.0973　and　0.0120,　respectively.