Extracting　coronary　arteries　is　important　in　clinical　applications　of　cardiac　Computed　Tomography　Angiography　(CTA).　However,　obtaining　an　accurate　segmentation　of　coronary　artery　is　challenging　because　of　complex　anatomy,　variation　in　image　quality,　as　well　as　motion　induced　by　heart　beating　and　respiration.　This　paper　presented　a　semi-automatic　framework　dedicated　to　coronary　artery　segmentation　in　3D+t　Computed　Tomography　Angiography　(CTA)　sequence.　The　proposed　segmentation　scheme　consists　of　two　parts:　vessel　centerline　extraction　and　vessel　shape　recovering.　For　the　starting　phase,　spherical　flux　based　minimal　path　method　was　employed　to　extract　the　main　centerlines　of　coronary　artery　tree.　To　implement　similar　centerline　extraction　scheme　automatically　in　subsequent　phases,　a　novel　method　key-points　detecting　method　was　proposed　and　an　endpoints　searching　procedure　was　taken.　In　this　process,　the　key-points　on　distal　vessels　are　easily　got　mismatched.　A　centerline　tracking　algorithm　constrained　by　patient-specific　vessel　length　was　used　to　complete　the　extraction.　The　the　overlap　(OV)　results　of　proposed　framework　are　93.56%　(LAD),　90.96%　(LCX)　and　93.76%　(RCA).　We　also　achieved　accuracy　(AC)　result:　0.6508mm　(LAD)　0.6141mm　(LCX)　and　0.6297mm　(RCA)　which　are　less　than　the　data　voxel　size　(0.68mm).　©　2020　IEEE.