The noise is one of the main factors affecting edge detection of the image. Various morphology operations can remove the noise effectively, and the study of algorithms using morphology to detect the edge of the image with noise is widely concerned in recent years. In order to improve the accuracy of edge detection and reduce the effect of noise on the image edge detection. An improved algorithm of morphology to resist the noise is proposed, using two different structure elements for edge detection. For the image with the salt and pepper noise, the improved algorithm can filter the noise effectively, the improved image is more smooth and clear outline. The edge location is accurate and the detail characteristics of the edge is well retained. The experiment results show that the algorithm has better anti-noise capacity, and the objective evaluation and visual effect are good. Meanwhile, the algorithm has certain practicality and feasibility.