The existing image segmentation algorithms based on Snake model generally have the disadvantages of poor noise robustness, limited application range, easy leakage of weak edge and difficult to converge to small and deep concave boundary of contour curve. In order to solve the problems, a novel image segmentation algorithm based on Snake model was proposed. Firstly, the Laplacian operator with isotropic smoothness was replaced by the new chosen diffusion term. Secondly, the p-Laplacian functional was introduced into the smooth energy term to strengthen the external force in the normal direction. Finally, the edge-preserving term was used to keep the external force field parallel to the edge direction, so as to prevent the weak edge from leaking and promote the contour curve to converge to the small and deep concave boundary. The experimental results show that, the proposed model not only overcomes the drawbacks of the existing image segmentation algorithms based on Snake model, possesses better segmentation effect, improves the anti-noise performance and corner positioning accuracy obviously, but also consumes less time. The proposed model is suitable for segmenting noise images, medical images, and natural images with many weak edges.