For detecting the edge of noise image, a new multiscale edge detection algorithm based on variogram function and directional wavelet is proposed. First, the criterions for the 45 degree and 135 degree directional edge in a image are proposed based on our previous research results and variogram function theory, respectively. Then, based on the direction of edges, an appropriate rotating parameter of directional wavelet is determined. The directional wavelet transform with different scales at different direction is implemented for different subregion. Thus, not only the accurate edge location is obtained, but also false edge points produced by noise and uneven gray scale in image are removed as much as possible. The results of simulation on the image contaminated badly by Gaussian noise indicate the performance of the proposed algorithm outperform the ones of the exist edge detection approaches with respect to maintaining edge and denoising.