The　separation　of　light　hydrocarbons　is　industrially　important　and　scientifically　challenging　due　to　their　high　similarity　in　physicochemical　properties.　Two-dimensional　metal-organic　frameworks　(2D　MOFs)　assembled　by　weak　supramolecular　interactions　are　more　likely　to　induce　structural　flexibility　and　exhibit　guest-dependent　gate-opening　behavior　than　3D　MOFs,　opening　new　horizons　for　LHs　storage　and　separation.　Here,　a　2D　MOF　(Cu-APC,　APC　=　2-aminopyrimidine-5-carboxylic　acid)　with　flexible-robust　interlayer　space　was　effectively　used　as　an　adsorbent　to　realize　C2　and　C3　hydrocarbons　separation.　Evidenced　by　gas　adsorption　isotherms　and　the　ideal　adsorbed　solution　theory　(IAST)　calculations,　Cu-APC　exhibits　moderate　C2H2/CO2　selectivity　(2.87),　high　C2H6/C2H4　selectivity　(2.27)　and　unique　multistep　adsorption　behavior　toward　C3H4/C3H6　at　ambient　conditions.　Moreover,　theoretical　calculations　revealed　that　C-H　&　sdot;&　sdot;&　sdot;N,　C=O　&　sdot;&　sdot;&　sdot;H-C,　and　C-H　&　sdot;&　sdot;&　sdot;it　interactions　are　formed　with　C2H2,　CO2,　C2H4,　and　C2H6　in　the　suitable　pockets　within　Cu-APC.　The　separation　performances　of　Cu-APC　for　C2H2/CO2,　C2H6/C2H4,　and　C3H4/C3H6　mixtures　were　also　confirmed　by　column　breakthrough　experiments.