The　density　functional　theory(DFT)　based　on　the　pseudo-potential　plane　wave　basis　was　employed　to　investigate　the　geometries,　electronic　structures,　linear　and　second-order　nonlinear　optical　properties　of　the　CuXY2(X=Ga,　In;　Y=S,　Se,　Te)　crystals　with　chalcopyrite　structure.　The　results　indicate　that　these　compounds　are　semiconductors　with　a　direct　gap　and　have　similar　band　structures.　The　static　dielectric　constants,　the　refractive　indices　and　the　second　harmonic　generation(SHG)　coefficients(d36)　of　these　compounds　increase　in　the　sequence　of　S→Se→Te　for　the　same　X　atom.　Among　the　occupied　bands,　those　states　near　the　top　of　the　valence　band　contribute　mostly　to　the　SHG　effect,　which　are　dominated　by　the　components　of　Cu3d　orbitals　and　the　valence　p　orbitals　of　Y　atom.　While　for　the　unoccupied　bands,　the　bands　mainly　derived　from　valence　p　orbitals　of　X　atoms　have　obvious　influences　on　the　SHG　coefficient.　Among　these　six　crystals,　CuInSe2　has　high　photoconductivity　and　better　absorption　of　sunlight.　In　addition,　CuGaS2　and　CuGaSe2　crystal　have　potential　applications　in　the　second-order　nonlinear　optical　fields　based　on　their　birefringences　and　SHG　strengths.　©　2019,　Higher　Education　Press.　All　right　reserved.