The coherent nature of radar illumination causes the speckle effect, which gives the synthetic aperture radar (SAR) image its noisy appearance. The probability distribution of speckle noise is multiplicative rather than additive, which makes the interpretation and processing of SAR imagery more difficult. A novel SAR image denoising method is proposed. First the multiplicative noise is transformed into additive‐like noise by logarithmic transformation. After that, a novel object function is proposed which combines a pre‐trained dictionary model to deal with the image. Finally, exponential transform is employed to recover the image. Experimental results show that the proposed method can effectively remove the noise of SAR images, and indicate good performance compared with other state‐of‐the‐art methods.