We propose an adaptive corner detector based on the degree of sharpness of the contour, which can detect the corners efficiently and accurately. First, we extract edges from an image using an edge detector, such as Canny, Sobel, etc. Second, we define a degree-of-sharpness variable and calculate its value for each point on the edge. Then we use an adaptive threshold of the degree of sharpness to find the initial corner candidates for each edge. Third, we propose a method of making a projection for an edge segment toward the edge's fitting line to remove salient points. Finally, if some neighboring corner candidates are detected in a support area, we offer an effective method to merge them into one point, and the final corners are reserved. The proposed detector is compared to a classical corner detector and two state-of-the-art methods on planar curves and gray-level images, respectively. The experimental results show that the proposed detector has high correctness in finding true corners. In addition, the algorithm is robust to the additive noise and can detect the circular contour well.