Geodesic　active　contour　(GAC)　model　is　a　common　used　method　for　image　segmentation.　But　one　drawback　of　this　model　is　that　it＇s　difficult　to　control　the　number　of　iterations　and　sometimes　may　produce　over-segmentation　results.　In　this　paper,　the　generalized　GVF　in　the　normal　direction　(GNGVF)　is　proposed,　and　an　improved　GAC　model　which　combines　GAC　with　GNGVF　is　proposed.　When　the　distance　between　the　evolution　curves　produced　by　successive　iterations　is　smaller　than　some　given　threshold,　the　on-off　function　will　change　and　different　force　will　affect.　The　new　force　can　extend　the　capture　range　and　stop　the　curve　at　the　boundary　stably　avoiding　over-segmentation.　The　experimental　results　show　the　curve　can　converge　to　boundary　well.