First-principles　density　functional　calculations　are　performed　to　study　the　geometries,　the　electronic　and　the　optical　properties　of　A(II)　Al2C4VI　(A　=　Zn　Cd,　Hg;　C　=　S,　Se)　semiconductors　each　with　a　defect　chalcopyrite　structure.　For　the　linear　optical　properties,　five　compounds　show　good　transmissions　of　light　in　the　IR　and　part　of　visible　regions,　and　among　them　HgAl2S4　and　HgAl2Se4　possess　moderate　birefringences.　For　the　nonlinear　optical　properties,　the　strong　second　harmonic　generation　(SHG)　response　can　be　expected　for　these　crystals,　and　the　large　static　SHG　coefficients　(＞　20　pm/V)　are　predicted　in　this　work.　The　SHG　response　of　A(II)　Al2C4VI　semiconductors　can　be　attributed　to　the　transitions　from　the　bands　near　the　top　of　valence　band　which　are　derived　from　S/Se　p　states　to　the　unoccupied　bands　that　are　contributed　by　p　states　of　Al　and　Hg　atoms.　By　comparing　with　the　optical　properties　of　the　commercialized　AgGaC2　crystals,　our　results　indicate　that　HgAl2S4　and　HgAl2Se4　compounds　are　good　candidates　for　the　second-order　nonlinear　optical　crystals　in　the　IR　region.