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In this paper, a novel despeckling method based on Gaussian scale mixtures (GSM) model in the directionlet domain is proposed. Before despeckling, we define a measurement of directivity of texture to calculate the directivity of texture according to the edge map. After directionlet transform, neighborhoods of coefficients at adjacent scales are modeled as GSM model. Under this model, a Bayes Least Squares (BLS) estimator is adopted to reduce speckle noise. Quantitative and qualitative experimental results show that the proposed method is an effective despeckling tool for SAR images. The method can suppress the speckle noise and, in the meantime, preserve the scene features as much as possible.