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 π conjugation could improve their stabilities. 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. that for either alkenes or alkynes, the systems substituted by phenyl have more stable intermediates because π conjugation could improve their stabilities.