This paper presents a local‐ and global‐statistics‐based active contour model for image segmentation by applying the globally convex segmentation method. We first propose a convex energy functional with a local‐Gaussian‐distribution‐fitting term with spatially varying means and variances and an auxiliary global‐intensity‐fitting term. A weight function that varies dynamically with the location of the image is applied to adjust the weight of the global‐intensity‐fitting term dynamically. The weighted total variation norm is incorporated into the energy functional to detect boundaries easily. The split Bregman method is then applied to minimize the proposed energy functional more efficiently. Our model has been applied to synthetic and real images with promising results. With the local‐Gaussian‐distribution‐fitting term, our model can also handle some texture images. Comparisons with other models show the advantages of our model.