Abstract: SAR image despeckling is a prerequisite for many SAR image processing tasks.In view of the problem of detail lost when using wavelet thresholding algorithm to despeckling，we present a despeckling algorithm based on morphological component anlysis (MCA) and overcomplete dictionary sparse representation. In this method，using the MCA theory，we separate the SAR image into piecewise smooth component，texture component and edge component.In the transform domain space，piecewise smooth component，texture component and edge component are respectively sparsely represented and despeckling by overcomplete dictionary including curvelet，and then SAR image is recovered out.Real SAR image is used for experiment and we compare our method with Lee filter method，wavelet threshold method and other existing methods.Experimental results show that our algorithm has better despeckling ability and keep more  useful detail information of the SAR image.