Three new ternary Ba-Sn-S system compounds, acentric Ba7Sn5S15, centric BaSn2S5, and centric Ba6Sn7S20 have been designed and synthesized by a conventional high-temperature solid-state reaction method using the evacuated silica tubes. The crystal structure of Ba7Sn5S15 shows the coexistence of a SnS4 tetrahedral and a Sn2S3 trigonal bipyramid. Importantly, the larger dipole moment of the [Sn2S3](2-) trigonal bipyramid group and the polarity enhancement of the bipyramidal arrangements result in a strong SHG effect at 2.05 mu m, which is 10 times of the SHG intensity of the benchmark AgGaS2 with the particle size of 30-46 mu m and twice as much as that with the particle size of 150-212 mu m. Evidently, the acentric Ba7Sn5S15 is a novel IR NLO crystal material with a wide mid-IR window and a strong SHG effect, which is the first reported among the Ba-Sn-S ternary system. Moreover, Ba2Sn5S15 can achieve type-I phase-matching that can be used for practical applications. In the centric BaSn2S5, all Sn atoms are coordinated by five S atoms to form novel SnS5 trigonal bipyramid polyhedrons. In the other centric Ba6Sn7S20, there is the coexistence of the two coordination patterns with a SnS5 trigonal bipyramid and SnS4 tetrahedral polyhedrons, featuring a special crystal structure in the Ba-Sn-S system.