In order to remove the thin cloud from remote sensing images, a remote sensing image was decomposed using a low-rank matrix and the properties of the thin cloud was analysed. The images were decomposed into the parts of background, foreground and thin cloud. Then, aimed objects could be obtained by combining the background with foreground informations. Experiments using different algorithms were carried out on satellite images and the effects of cloud removal were measured by subjective and objective indexes. The experiment results illustrate that the method can eliminate the defects in conventional methods effectively. In different scenarios, it can not only effectively remove thin cloud from image of remote sensing efficaciously, but also retain the details of the objects.