Edge detection is important in many fields such as pattern recognition and computer vision. Many edge detection methods are sensitive to noises because gradients are used to enhance edges. To solve this problem, a new edge detection method is proposed in the paper based on local self-similarity. For any pixel in an image, a metric, called as local self-similar coefficient, is defined on its square neighborhood. The square neighborhood blocks are classified into three types: edge block, smooth block and random block. Two theorems have been proven according to the self-similar metric definition and the image block classification. The theorems and experimental results demonstrate that the local self-similar coefficients on edge blocks and smooth blocks are much greater than that on random blocks. Fortunately, it is quite easy to distinguish edge blocks from smooth blocks. A new edge detection algorithm based on these properties is provided in the paper. Several kinds ofimages, including human pictures and natural scenery, are used to detect edges with the new algorithm, and satisfactory results are obtained. The results show that under noisy conditions, the new algorithm extracts better edges than Sobel method.