In order to preserve the SAR image edge characteristics and improve the suppression performance of multiplicative speckle noise in SAR image, a new despeckling algorithm based on iterative direction filtering is proposed. Firstly, the ratio Edge Strength Map (ESM) and direction information are estimated by Gaussian-Gamma-shaped bi-windows, and anisotropic support domain along the ESM direction is obtained with the ESM and direction information to adaptively control the Anisotropic Gaussian Kernel (AGK) in rectangular local window. Secondly, the decay factor is obtained by combining several local statistics, and the negative-exponential weighting coefficients are produced by the decay factor and are adaptive to the characteristics of regional distribution of SAR image. Thirdly, direction filtering is formed by combining the negative-exponential weighting coefficients and the local window with anisotropic support domain and different directions. Finally, speckle suppression in SAR image with edge protection can be realized by iterative operation of direction filtering. The experimental results show that, compared with most existing despeckling algorithms, the proposed algorithm achieves better performance in the speckle suppression and image edge preservation.