Active contour model is widely used in image segmentation and object contour extraction, and the edge-based Geodesic Active Contour (GAC) model is widely used in the object extraction with obvious edges. But the process of GAC evolution costs many iterations and long time. In order to solve the problems, the GAC model was improved with Bessel filter theory. Firstly, the image was smoothed by Bessel filter to reduce the noise. Secondly, a new edge stop term was constructed based on the edge detection function of Bessel filter and incorporated into the GAC model. Finally, the Reaction Diffussion (RD) term was added to the constructed model for avoiding re-initialization of the level set. The experimental results show that, compared with several edge-based models, the proposed model improves the time efficiency and ensures the accuracy of segmentation results. The proposed model is more suitable for practical applications.