The segmentation of synthetic aperture radar (SAR) images is a challenging task. The difficulty lies in that the existence of speckle noise leads to the segmentation of small sets of isolated pixels.To solve this problem,a local smoothing weighted graph cut model is pre sented in this paper. Firstly,a smoothness regularization term is introduced into the weighted graph cut model.As a result,the robustness of the spectral clustering based SAR image segmentation methods to sp eckle noise is improved and small sets of isolated pixels are restrained.Secondly,using the e quivalence relation between the weighted graph cut model and weighted kernel K-means,kernel mappin g is added to the objective function of local smoothing weighted graph cut model with a different fashion from parametric kernel graph cuts,and the label function can be solved via graph cut optimizatio n algorithm.The method avoids calculating graph spectrum,which is a key step of spectral clustering ba sed SAR image segmentation methods.Meanwhile,it makes up for the deficiency of parametric ke rnel graph cuts method when the segmentation number is two.Experimental results with simulated a nd real-world SAR images demonstrate that the proposed method is effective and provides comparable or bet ter results than the classical graph cut based methods.