Because the color is a powerful indicator of a color image, so the color edge detection is essensial for color image segmentation. The speckle noise in a color image would severely degrade the image interpretation and increase the difficulty for image processing, such as for edge detection and feature extraction. Thus, it is important to reserve the edge characters effectively based on speckle noise removing. This paper proposes a novel algorithm for removing the speckle noise and detecting the color image edge. Firstly, a denoising algorithm is proposed based on the alpha stable distribution. Secondly, the color image edges are obtained automatically by combining an improved isotropic edge detector and a fast entropy threshold technique. According to the color distance between the pixel and its eight neighbor-pixels, the color image edges can be further accurately determined. The experiments demonstrate that the proposed method can successfully be used to obtain the color image edges.