Two interesting non-centrosymmetric metal chalcogenides, Rb2Ag3Sb3 S-7 and Cs2Ag3Sb3S7, were synthesized by an ionothermal approach. Crystals of compounds Rb2Ag3Sb3S7 and Cs2Ag3Sb3S7 possess isomorphic configuration, consisting of two-dimensional (2D) anionic networks (infinity)[Ag3Sb3S7](2-), which are split by alkali-metal M+ cations. The band gaps are 2.11 and 2.02 eV for Rb2Ag3Sb3S7 and Cs2Ag3Sb3S7, respectively. Second-harmonic generation (SHG) studies revealed that Rb2Ag3Sb3S7 affords a powder SHG performance of similar to 0.5 x AgGaS2 with type-I phase matching, while Cs2Ag3Sb3S7 shows a slightly stronger SHG performance of similar to 0.6 x AgGaS2 with type-I phase matching. Both compounds possess broad transparency ranges (similar to 0.6-20 mu m), suggesting their potential as infrared (IR) nonlinear optical (NLO) materials. The laser damage thresholds (LDTs) of both Rb2Ag3Sb3S7 and Cs2Ag3Sb3S7 are about 2.3 x AgGaS2. The calculated birefringence indexes Delta n are 0.1885 and 0.1944 at 1.064 mu m, respectively, which are sufficiently large enough to achieve phase matching. Theoretical studies using density functional theory have been implemented to further understand the relationship between their NLO properties and band structures.