This paper introduces SAMAug, a novel visual point augmentation method for the Segment Anything Model (SAM) that enhances interactive image segmentation performance. SAMAug generates augmented point prompts to provide more information to SAM. From the initial point prompt, SAM produces the initial mask, which is then fed into our proposed SAMAug to generate augmented point prompts. By incorporating these extra points, SAM can generate augmented segmentation masks based on the augmented point prompts and the initial prompt, resulting in improved segmentation performance. We evaluate four point augmentation techniques: random selection, maximum difference entropy, maximum distance, and a saliency model. Experiments on the COCO, Fundus, and Chest X-ray datasets demonstrate that SAMAug can boost SAM's segmentation results, especially using the maximum distance and saliency model methods. SAMAug underscores the potential of visual prompt engineering to advance interactive computer vision models.