Two new mid-infrared transparency compounds, centric Ba2BiGaS5 (1) and acentric Ba2BiInS5 (2), were synthesized from a high-temperature solid-state reaction in evacuated closed silica tubes. Their crystal structures were determined by a single crystal X-ray diffraction method at 293 K. The results of crystal structure solution indicate that compound 1 crystallize; in the centrosymmetric space group Pnma with trans- (infinity-)(1) [BiGaS5](4-) chain structure, while compound 2 crystallizes in the noncentrosymmetric polar space group Cmc2(1) with cis- (infinity)(1)[BiInS5](4-) chain structure. Two types of lone-pair electrons alignment fashions within (infinity-)(1) [BiMS5](4-) chains result in destructive (for 1) or constructive (for 2) dipole moments, as illustrated in the crystal structures and the partial electron density maps based on the first-principles electronic structure computations. Powder second-harmonic generation (SHG) experiments with a 2.05 mu m pumping laser show that the SHG efficiency of the polar compound 2 is approximately 0.8 times that of KTiOPO4 (KTP) reference. Furthermore, SHG signal intensity measurements using different size particles of powder samples indicate that compound 2 can also achieve type I phase-matching, which makes the compound promising for practical applications.