The　addition　reactions　of　alkenes　and　alkynes　to　the　H-terminated　GaN　(0001)　surface　with　a　Ga　dangling-bond　have　been　studied　employing　periodic　density　functional　theory　(PDFT)　calculations.　Detailed　information　on　the　reaction　pathways　of　these　alkenes　and　alkynes　with　H-GaN　(0001)　surface　is　provided,　which　indicates　that　the　reactions　contain　two　steps　separated　by　the　metastable　intermediates:　elementary　addition　reaction　and　H-abstraction　process.　From　the　energy　curves,　the　reactions　are　clearly　viable　in　the　cases　of　ethene,　styrene　and　phenylacetylene;　while　for　ethyne,　the　H-abstraction　barrier　is　higher　than　the　desorption　barrier　of　the　intermediate,　so　the　adsorbed　C2H2　in　intermediate　is　more　likely　to　be　desorbed　back　into　the　gas　phase　than　to　form　a　stable　adsorbed　species.　Furthermore,　it　is　obvious　that　for　either　alkenes　or　alkynes,　the　systems　substituted　by　phenyl　have　more　stable　intermediates　because　pi　conjugation　could　improve　their　stabilities.