Synthetic Aperture Radar (SAR) images are inherently affected by a multiplicative noise-like phenomenon called speckle, which is indeed the nature of all coherent systems. Speckle decreases the performance of almost all the information extraction methods such as classification, segmentation, and change detection, therefore speckle must be suppressed. Despeckling can be applied by the multilooking method when the image is formed or by spatial filters after the image formation. However, multilooking decreases the spatial resolution. Moreover, the performance of spatial filters depends on the size and the orientation of used window’s kernel. To overcome these limitations, Multi-Resolution Analysis (MRA), e.g., Wavelet Transform (WT), can be used. In this article, based on the intra-scale and inter-scale dependencies of wavelet coefficients and by employing the Maximum a Posteriori (MAP) estimator, a method for denoising the wavelet coefficients was proposed. Distributions of noise and noise-free wavelet coefficients in wavelet domain were considered as bivariate Gaussian and bivariate circular symmetric Laplace PDFs, respectively. For comparison analysis, Lee and Frost filters were used, also several classical thresholding methods such as VisuShrink, SureShrink, and BayesShrink were employed. Peak Signal-to-Noise Ratio (PSNR) and edge-preserving index beta were used to evaluate the simulated SAR data. Also, Equivalent Number of Looks (ENL) was employed for real SAR data. Experimental results showed that the proposed despeckling method performed more efficiently to suppress the speckle and preserve the edges than others. For instance, the PSNR and beta values that computed for 16 looks simulated SAR data were equal to 30.42 and 0.734, respectively. Also, the ENL values for region 1 of Noerdlinger and San Francisco images corresponded to 71.12 and 34.57, respectively.