This paper is devoted to decomposing one given image into the cartoon and texture. The cartoon parts correspond to the main large objects in the image, and the textural parts contain fine scale details. Mathematically, these two components should belong to the different function spaces corresponding to different norms. In most variational models of image decomposition, the cartoon parts are described by the total variation norm and the texture parts are characterized by its dual norm. Using these methods, the cartoon and texture can be separated from the original image. Some structures, such as edges, are well preserved in the cartoon image. However, as far as we know, none of these methods considers the geometric characteristics information of the texture position in the separated cartoon images. That is, the geometrical information in those separated cartoon images may have been destroyed, which can be seen from the experiments in this paper. To maintain these geometrical characteristics, we introduce one smoothed vector field and let it approximate to the negative gradient direction of the cartoon image, and then for the smoothed vector field, we let it belong to the Lebesgue space, thus a new variational decomposition model is proposed. The corresponding alternating direction method is discussed in detail. Experimental results are reported to show the visual qualities compared with other methods.