Although　numerous　superior　nonlinear　optical　(NLO)　crystals　for　the　UV-vis　to　the　near-infrared　(IR)　region　have　been　established,　the　development　of　an　efficient　NLO　material　capable　of　broadband　second　harmonic　generation　(SHG)　in　the　mid-IR　region　is　still　a　big　challenge.　In　this　work,　we　performed　hybrid　functional　calculations　to　accurately　assess　the　mid-IR　NLO　capabilities　of　a　group　of　I3-V-VI4　compounds　(with　I　=　Ag　or　Cu,　V　=　P　or　As,　and　VI　=　S　or　Se).　The　linear　and　nonlinear　optical　properties　of　these　crystals　were　predicted　and　analyzed.　This　group　of　compounds　display　moderate　optical　anisotropy　of　refraction　(0.1　>　Δn　>　0.03)　to　fulfill　the　phase-matching　conditions.　In　particular,　the　static　SHG　coefficients　of　Cu3AsS4,　Ag3PSe4　and　Cu3PSe4　are　predicted　to　be　about　twice　that　of　the　benchmark　AgGaSe2.　A　detailed　analysis　of　their　precise　electronic　structures　and　local　dipole　moments　suggests　that　it　is　the　coupling　of　the　large　dipole　moment　vector　of　the　constituent　asymmetry　[I-VI4]　tetrahedron　and　the　strong　covalent　character　between　V　and　VI　ions　that　contributes　to　the　large　SHG　response.　These　candidates　would　promote　the　development　of　the　mid-IR　NLO　functional　materials.　©　The　Royal　Society　of　Chemistry.