With the high-speed development of digital image processing technology, machine vision technology has been widely used in automatic detection of industrial products. A large amount of products can be treated by computer instead of human in a shorter time. In the process of automatic detection, edge detection is one of the most commonly used methods. But with the increasing demand for detection precision,traditional pixel-level methods are difficult to meet the requirement, and more subpixel level methods are in the use. This paper presents a new method to detect curved edge with high precision. First, the target area ratio of pixels near the edge is computed by using one-dimensional edge detection method. Second, parabola is used to approximately represent the curved edge. And we select appropriate parameters to obtain accurate results. This method is able to detect curved edges in subpixel level, and shows its practical effectiveness in automatic measure of products with arc shape in large industrial scene.