The　first-principles　density　functional　calculations　are　performed　to　study　the　geometries　and　electronic　structures　of　HgGa2X4　(X　=　S,　Se,　Te)　semiconductors　with　defect　chalcopyrite　structures,　and　the　optical　properties　of　all　crystals　are　investigated　systematically.　The　results　indicate　that　these　compounds　have　similar　band　structures　and　the　band　gap　decreases　from　S　to　Se　to　Te.　For　the　linear　optical　properties,　three　crystals　show　good　light　transmission　in　the　IR　and　part　visible　regions,　and　in　particular,　HgGa2S4　and　HgGa2Se4　crystals　possess　moderate　birefringence.　For　the　nonlinear　optical　properties,　these　crystals　have　stronger　second　harmonic　generation　(SHG),　and　are　theoretically　predicted　to　have　larger　second-order　static　SHG　coefficients　(＞　30　pm/V).　The　SHG　of　HgGa2X4　(X　=　S,　Se,　Te)　semiconductors　can　be　attributed　to　the　transitions　from　the　bands　near　the　top　of　valence　band　derived　from　X　(X　=　S,　Se,　Te)　p　states　to　the　unoccupied　bands　contributed　by　the　p　states　of　Ga　atoms.　Our　results　indicate　that　the　HgGa2S4　and　HgGa2Se4　compounds　are　good　candidates　for　nonlinear　optical　crystals　in　the　IR　region.