Delineating the lesion area is an important task in image-based diagnosis. Pixel-wise classification is a popular approach to segmenting the region of interest. However, at fuzzy boundaries such methods usually result in glitches, discontinuity, or disconnection, inconsistent with the fact that lesions are solid and smooth. To overcome these undesirable artifacts, we propose the BezierSeg model which outputs bezier curves encompassing the region of interest. Directly modelling the contour with analytic equations ensures that the segmentation is connected, continuous, and the boundary is smooth. In addition, it offers sub-pixel accuracy. Without loss of accuracy, the bezier contour can be resampled and overlaid with images of any resolution. Moreover, a doctor can conveniently adjust the curves control points to refine the result. Our experiments show that the proposed method runs in real time and achieves accuracy competitive with pixel-wise segmentation models.