The speckle noise in synthetic aperture radar (SAR) image is difficult to refract the scattering characteristics of the irradiated area accurately, and increases the difficulty of the target feature extraction. The traditional despeckle method reduces the noise, but it leads to the loss of the details of the image at the same time. However, the denoising method based on the Three Dimensional Matching Block (BM3D) utilizes the sparse representation in the transform domain, which divides the image into a threedimensional space. By analyzing the characteristics of the model and setting the parameters, the BM3D algorithm is applied to the SAR image. Compared with the traditional methods, it is found that the BM3D algorithm can be successfully applied to the SAR image, the edge stay index reaches 0.4845, which can suppress the speckle and preserve the details of the image, and the effectiveness of the algorithm is verified.