This paper proposes a quadric fitting polynomial texture mapping model based on moving least squares. The proposed model is mainly applied in image deformation techniques using control meshes. The shape in the image is firstly embedded into a control mesh which is deformed. Then the deformed shape is rendered by using texture mapping on the control mesh. Displaces of the vertices in the control mesh are treated as known function values. The MLS method is used to compute the quadric function for texture mapping. Compared with texture mapping using linear function, the method proposed can greatly improve the smoothness of the texture mapping function, and the deformation result is more natural and physically plausible.