The present invention provides an SAR (synthetic aperture radar) image coherent speckle suppression method. According to the method, the probability density function of multiplicative noises and prior information are utilized to construct the approximation term, diffusion term and sparse constraint of a model; a sparse partial differential equation model is established; and alternate optimization is adopted to obtain a solution, so that a coherent speckle-suppressed SAR image can be obtained. With the sparse partial differential equation-based SAR image coherent speckle suppression method of the invention adopted, the defects of a traditional filtering method and a partial differential equation method can be eliminated; and the coherent speckles of the image can be suppressed, the radiation resolution of the SAR image can be improved, and at the same time, the edge information and scattering characteristics of a radar target can be well retained, the quality improvement of the SAR image can be realized effectively, the numerical solution of the model can be obtained robustly, and therefore, the method is easy to implement.