The traditional active contour models can hardly achieve the accurate river segmentation of SAR images. To solve this problem, a novel active contour model with weighted exponential region energy is proposed, which can extract rivers in SAR images accurately. The exponential region energy is incorporated into the energy functional of the Chan-Vese model, which can measure the difference between the segmented image and the original image, resulting in the improvement of segmentation accuracy of the model. In addition, the maximum absolute differences of the pixel grayscale values inside the object and background regions are utilized to replace the original constant region energy weights, which can adaptively adjust the ratios of the object and background region energies and accelerate the motion of the curve towards the boundaries of the object region, resulting in the higher segmentation efficiency. The experiments are performed on real SAR images of rivers and results demonstrate that compared with the traditional active contour models, the proposed model can segment rivers in SAR images more rapidly and accurately and has some advantages in terms of both segmentation performance and segmentation efficiency.