Synthetic aperture radar (SAR) images are contaminated by multiplicative speckle noise, which reduces the contrast and resolution of the images. To improve the quality and the performance of quantitative image analysis, speckle reduction is a prerequisite for SAR images. In this paper, a new method is proposed by calculating the expected value of all the pixel elements in the window with respect to the centre pixel. The weighted mean of all the expected values in the window replaces the centre pixel. The weights are calculated according to the height of the probability distribution. Thus, the expected value which has higher probability has more weightage. The proposed method is applied to the air-borne and space-borne SAR images. By comparing with some well-known filters, the obtained results demonstrate that the proposed method is able to reduce the noise effectively with accurately preserving edges and fine details of the images.