In this paper, we present a Stationary Wavelet Transform (SWT) based method for the purpose of despeckling the Synthetic Aperture radar (SAR) images by applying a maximum a posteriori probability (MAP) condition to estimate the noise free wavelet coefficients. The solution of the MAP estimator is based on the assumption that the wavelet coefficients have a known distribution. Rayleigh distribution is used for modeling the speckle noise and Laplacian distribution for modeling the statistics of the noise free wavelet coefficients for the purpose of designing the MAP estimator. Rayleigh distribution is used for modeling the speckle noise since speckle noise can be well described by it. The parameters required for MAP estimator is determined by the technique used for parameter estimation after SWT. The experimental results show that the proposed despeckling algorithm efficiently removes speckle noise from the SAR images