Noncentrosymmetric　(NCS)　metal-chalcogenides　have　emerged　as　a　candidate　for　infrared　nonlinear　optical　(IR-NLO)　materials,　but　it　remains　an　enormous　challenge　to　achieve　simultaneously　a　large　second-harmonic-generation　(SHG)　coefficient　(d(ij)),　strong　laser-induced　damage　threshold　(LIDT),　wide　phase-matching　(PM)　range,　and　low　melting　point　(MP)　in　a　single　material.　Herein,　a　novel　ternary　mixed-metal　chalcogenide,　Sn2Ga2S5,　was　prepared　via　a　facile　mid-temperature　fluxing　method.　It　adopts　a　polar　space　group　Pna2(1)　(no.　33)　and　shows　a　distinctive　3D　NCS　network　made　by　(2)(infinity)[Ga2S54-]　layers　and　(1)(infinity)[Sn2S68-]　chains　via　the　sharing　of　common　corners.　Significantly,　Sn2Ga2S5　exhibits　an　excellent　comprehensive　performance　for　IR-NLO　applications　that　surpasses　the　current　benchmark　of　AgGaS2,　including　a　strong　SHG　response　d(ij)　(2.5　X　AgGaS2),　high　LIDT　(6.6　x　AgGaS2),　wide　PM　range　(＞725　nm),　broad　transparent　region　(0.57-13.8　mu　m),　and　low　MP　(ca.　958　K).　Furthermore,　the　detailed　theoretical　calculation　results　elucidate　that　the　strong　d(ij)　of　Sn2Ga2S5　can　be　ascribed　to　the　combined　effect　of　two　asymmetric　building　motifs　(ABMs),　that　is,　dimeric　[Sn2S6]　and　[Ga2S5]　units.　Such　a　systematic　work　would　provide　some　useful　guidance　for　the　prediction　and　discovery　of　new　IR-NLO　chalcogenides　with　mixed　ABMs.