Abstract: SAR image despeckling is always a key and indispensable step in SAR image preprocessing. The Bilateral Filtering (BF), which combines grey similarity and spatial closeness to reduce noise, is introduced to SAR image despeckling recently. However, when BF is directly used for SAR image despeckling, it is hard to select the optimal spatial closeness variance and imprecise to measure the grey similarity by Gaussian function, so an Adaptive Bilateral Filter (ABF) is proposed. The ABF adjusts spatial closeness variance to the local coefficient of variation and calculates the grey similarity of SAR image by the likelihood probability function instead of the Gaussian function. The tests on synthesized and real SAR images show that the ABF can notably smooth speckles with imperceptible details pollution, which achieves better performance than that of the other related methods.