The　band　structure,　density　of　states　of　AlxGa1-xN　and　InyGa1-yN　was　performed　by　the　first-principles　method　within　the　local　density　approximation.　The　calculated　energy　gaps　of　the　AlN,　Al0.5Ga0.5N,　GaN,　In0.5Ga0.5N　and　InN　were　5.48,　4.23,　3.137,　1.274　and　0.504　eV,　which　were　in　agreement　with　the　experimental　result.　The　dielectric　functions,　absorption　coefficient　and　loss　function　were　calculated　based　on　Kramers-Kronig　relations.　Further　more,　the　relationships　between　electronic　structure　and　optical　properties　were　investigated　theoretically.　For　AlxGa1-xN　and　InyGa1-yN　materials,　the　micromechanism　of　the　optical　properties　were　explained.