Cast shadow on the background is generated by an object moving between a light source and the background. The position and illumination of the source always change with time, while the background is stable. Therefore, features connected with light source always change with time, such as geometry and color. In this paper, we present a shadow removal method by homomorphic model to extract surface reflectance component, which is only connected with background of the scene and is robust to change of light source. We assume that reflectance component fits Gaussian distribution, and then use GMM to model it. Experimental results show that, except dealing with shadow, our method is not sensitive to the change of illumination.