Development　of　earth-abundant,　low-cost　and　easily　synthesizable　catalysts　for　the　semi-hydrogenation　of　acetylene　is　urgently　needed.　Here,　we　have　systematically　investigated　the　structure,　electronic　properties,　hydrogen　dissociation,　and　acetylene　semi-hydrogenation　activity　and　selectivity　of　poly(heptazine　imide)　(PHI)　loaded　with　different　sizes　of　Cun　(n　=　1,2,4,13)　clusters　(Cun/PHI)　by　density　functional　theory　calculations.　The　results　show　that　Cu4/PHI　with　tetrahedral　configuration　has　a　better　hydrogenation　activity　in　the　acetylene　semi-hydrogenation　reaction　with　H　adsorbed　in　the　vicinity　of　acetylene　and　subsequent　intermediates　in　a　nonbridge　position,　resulting　in　a　smaller　hydrogenation　energy　barrier.　In　addition,　the　top　Cu　atom　transfers　a　large　number　of　electrons　to　the　bottom　Cu　atoms　and　PHI,　and　only　a　small　number　of　electrons　transfer　to　ethylene,　resulting　in　weak　adsorption　of　ethylene　and　easy　desorption,　which　makes　it　good　selectivity　and　therefore　it　can　be　used　as　a　candidate　catalyst　for　the　semi-hydrogenation　of　acetylene.　This　study　provides　insights　into　the　design　of　catalysts　with　suitable　size　clusters　loaded　on　carbon　nitride　materials　for　efficient　acetylene　semihydrogenation　reactions.