There were some difficulties when applying current geometric deformable models to color image segmentation. In order to solve the problem, different edge detectors are compared, and then CGAC-an improved geometric deformable model is developed by applying a new edge detector from Di Zenzo multivalued geometry of color image to GAC. The experimental results show that when applying GAC channel by channel directly to color image segmentation, different boundaries of the same object represented by zero level sets in different channels can be obtained but they can not be identified which boundary is the exact boundary of object. On the contrary, when the evolution of zero level sets stops by applying CGAC, ideal boundary of object, which coincides with human perception, is obtained.