In　this　paper,　a　level　set　method　is　proposed　for　the　segmentation　of　Left　Ventricle　(LV)　from　short-axis　cardiac　magnetic　resonance　images.　According　to　the　anatomical　knowledge　of　LV,　we　first　propose　a　convexity　preserving　mechanism　to　keep　the　shape　of　the　evolving　contour　convex　during　the　curve　evolution,　and　thereby　improves　the　segmentation　accuracy.　Then,　the　mechanism　is　incorporated　into　two　layer　level　set　method　to　delineate　endocardial　and　epicardial　boundaries　simultaneously.　The　proposed　method　has　been　quantitatively　validated　on　a　public　dataset,　and　experimental　results　and　comparisons　with　other　methods　demonstrate　the　superior　performance　of　our　method.　Furthennore,　such　a　generally　constrained　convexity-preserving　level　set　method　can　be　useful　in　many　other　potential　applications,　as　validated　by　experiments.