Two new quaternary pnictide-based multinary compounds, Ba 4 AgGa 5 P 8 and Ba 4 AgGa 5 As 8 , were synthesized from the Pb-flux reactions. By using the single crystal X-ray diffraction technique the structures are determined to crystallize in a new type with the noncentrosymmetric (NCS) space group Iba2 (No. 45) (cell parameters: a = 7.294(9)/7.4769(8) Å, b = 18.03(2)/18.5766(19) Å, c = 6.557(8)/6.7590(7) Å for the P-and As-containing compounds, respectively. Theoretical calculations indicate strong SHG responses for both compounds, which are approximately two times larger than that of AgGaSe 2 . Based on the calculated cutoff-energy-depending static SHG coefficients, the large NLO coefficients of these compounds should originate from the distorted GaPn 4 tetrahedra, which construct various layers and chains giving rise to a large polarization. Both compounds have moderate birefringence (Δn), 0.157 and 0.206 for Ba 4 AgGa 5 P 8 and Ba 4 AgGa 5 As 8 , respectively, suitable for the phase-matching condition in the SHG process.