Density　functional　theory　(DFT)　based　on　the　pseudo-potential　plane　wave　basis　set　was　used　to　investigate　the　electronic　structures　and　optical　properties　of　CuAlX2　(X=S,　Se,　Te)　crystals　with　a　chalcopyrite　structure.　The　results　indicate　that　these　compounds　have　a　similar　band　structure　and　the　bandgap　decreases　from　S　to　Te.　Except　for　the　static　birefringence,　which　is　just　opposite　to　a　change　in　the　bandgap,　the　static　dielectric　constant,　refractive　index　and　second　harmonic　generation　(SHG)　coefficient　d(36)　of　this　series　of　compounds　increased　from　S　to　Te.　The　SHG　response　of　the　three　semiconductors　can　be　attributed　to　transitions　from　the　occupied　bands　near　the　top　of　the　valence　band　to　the　unoccupied　bands　that　are　contributed　to　by　the　p　states　of　the　Al　and　X　atoms.　Among　the　three　crystals,　the　optical　properties　of　the　CuAlTe2　crystal　are　better　than　those　of　CuAlS2　and　CuAlSe2　crystals　except　that　the　corresponding　static　birefringence　is　too　small.