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.