Some classical filters, such as bilateral filter, nonlocal means (NLM) filter, and locally adaptive regression kernel, have proven to have a good performance in image denoising. However, there is one shortcoming, i.e., they cannot control the denoising strength very well. As for synthetic aperture radar (SAR) images, due to the special multiplicative noise, the denoising process becomes more complicated. A diffusion iterative filter can enhance the performance of a kernel in the denoising process but will lose some latent details and important targets from the underlying SAR image. In contrast, an iterative boosting filter can preserve these latent details of the SAR image well, although the improvement of the kernel performance is not very desired. By adopting the advantages of diffusion and boosting of the two iterative methods, an adaptive iterative risk estimator minimum mean square error (Min-MSE) method is proposed, which is mainly based on the Min-MSE to adaptively get the optimal iterative method and the corresponding optimal iterative number. The analysis of the experimental results and the comparison with some other state of the art methods demonstrate that our proposed method can improve the performance of an NLM filter and effectively suppress the SAR image speckle.