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Multiplicative noise (also known as speckle noise) often exists in several image systems, such as synthetic aperture radar (SAR), sonar, ultrasound and laser imaging. In this paper, we proposed a novel variational model for multiplicative noise removal by combining the nonlocal total variation (NLTV) and the Weberized total variation (TV). A main advantage of the NLTV over classical TV norm is the superiority in dealing with better textures and repetitive structures. The Weberized TV considers the influence of the background intensity, thereby can improve the performance when some small fine details appear in the background of the original image. Moreover, we develop a primal-dual hybrid gradient (PDHG) algorithm to solve the proposed model. A set of experiments on synthetic and real images demonstrate that the proposed method is able to preserve accurately edges and structural details of the image.