To preserve the sharp features and details of the synthetic aperture radar (SAR) image effectively when despeckling, a despeckling algorithm with edge detection in nonsubsampled second generation bandelet transform (NSBT) domain is proposed. First, the Canny operator is utilized to detect and remove edges from the SAR image. Then the NSBT which has an optimal approximation to the edges of images and a hard thresholding rule are used to approximate the details while despeckling the edge-removed image. Finally, the removed edges are added to the reconstructed image. As the edges are detected and protected, and the NSBT is used, the proposed algorithm reaches the state-of-the-art effect which realizes both despeckling and preserving edges and details simultaneously. Experimental results show that both the subjective visual effect and the mainly objective performance indexes of the proposed algorithm outperform that of both Bayesian wavelet shrinkage with edge detection and Bayesian least square-Ganssian scale mixture (BLS-GSM).