In　this　article,　we　propose　a　visual　simultaneous　localization　and　mapping　(SLAM)　method　by　predicting　and　updating　line　flows　that　represent　sequential　2-D　projections　of　3-D　line　segments.　While　feature-based　SLAM　methods　have　achieved　excellent　results,　they　still　face　problems　in　challenging　scenes　containing　occlusions,　blurred　images,　and　repetitive　textures.　To　address　these　problems,　we　leverage　a　line　flow　to　encode　the　coherence　of　line　segment　observations　of　the　same　3-D　line　along　the　temporal　dimension,　which　has　been　neglected　in　prior　SLAM　systems.　Thanks　to　this　line　flow　representation,　line　segments　in　a　new　frame　can　be　predicted　according　to　their　corresponding　3-D　lines　and　their　predecessors　along　the　temporal　dimension.　We　create,　update,　merge,　and　discard　line　flows　on-the-fly.　We　model　the　proposed　line　flow　based　SLAM　(LF-SLAM)　using　a　Bayesian　network.　Extensive　experimental　results　demonstrate　that　the　proposed　LF-SLAM　method　achieves　state-of-the-art　results　due　to　the　utilization　of　line　flows.　Specifically,　LF-SLAM　obtains　good　localization　and　mapping　results　in　challenging　scenes　with　occlusions,　blurred　images,　and　repetitive　textures.