In　this　paper,　an　improved　fuzzy　connectedness　(PC)　method　was　proposed　for　automatic　three-dimensional　(3D)　liver　vessel　segmentation　in　computed　tomography　(CT)　images.　The　vessel-enhanced　image　(i.e.,　vesselness　image)　was　incorporated　into　the　fuzzy　affinity　function　of　FC,　rather　than　the　intensity　image　used　by　traditional　FC.　An　improved　vesselness　filter　was　proposed　by　incorporating　adaptive　sigmoid　filtering　and　a　background-suppressing　item.　The　fuzzy　scene　of　FC　was　automatically　initialized　by　using　the　Otsu　segmentation　algorithm　and　one　single　seed　generated　adaptively,　while　traditional　FC　required　multiple　seeds.　The　improved　FC　method　was　evaluated　on　40　cases　of　clinical　CT　volumetric　images　from　the　3Dircadb　(n　=　20)　and　Sliver07　(n　=　20)　datasets.　Experimental　results　showed　that　the　proposed　liver　vessel　segmentation　strategy　could　achieve　better　segmentation　performance　than　traditional　FC,　region　growing,　and　threshold　level　set.　Average　accuracy,　sensitivity,　specificity,　and　Dice　coefficient　of　the　improved　FC　method　were,　respectively,　(96.4　+/-　1.1)%,　(73.7　+/-　7.6)%,　(97.4　+/-　1.3)%,　and　(67.3　+/-　5.7)%　for　the　3Dircadb　dataset　and　(96.8　+/-　0.6)%,　(89.1　+/-　6.8)%,　(97.6　+/-　1.1)%,　and　(71.4　+/-　7.6)%　for　the　Sliver07　dataset.　It　was　concluded　that　the　improved　FC　may　be　used　as　a　new　method　for　automatic　3D　segmentation　of　liver　vessel　from　CT　images.