This paper addresses the problem of automatic fitting of feature points for border detection of skin lesions. This problem is an important task in segmentation of dermoscopy images for semi-automatic early diagnosis of melanoma and other skin lesions. Given a set of feature points selected by a dermatologist, we apply a powerful nature-inspired metaheuristic optimization method called bat algorithm to obtain the free-form parametric Bezier curve that fits the points better in the least-squares sense. Our experimental results on two examples of skin lesions show that the method performs quite well and might be applied to automatic fitting of feature points for border detection in medical images.