In order to overcome the problem that difficult to accurately estimate the contrast and width of the edge, and easy to be affected by noise, which resulting in the reduction of the edge extraction accuracy in the current edge detector. A multi-scale differential edge detection algorithm with invariant scale and contrast was designed. Firstly, a mathematical function was used to represent the edge and to calculate the position, width, contrast, offset and direction of the closed form. The noise was filtered out as a low contrast feature. Secondly, a precise scale normalization method is defined to make the features of different dimensions comparable and improve the accuracy of the classifier. Then, through the derivative of gradient amplitude squared and the Laplaian calculation of gradient amplitude squared, the influence of contrast parameters was eliminated, and the edge detector with constant scale and contrast was constructed to output the edge. Experimental results show that the proposed method presents higher edge extraction effect, and the edge is more clear and complete compared with the current edge detection technology.