Inspired from the idea of data representation in manifold learning, we derive a novel model which combines the original training images and their tangent vectors to represent each image in the testing set. Different from the previous methods, the L1 norm is used to control the reconstruction error. Considering the fact that the objective function in the proposed model is non-smooth, we utilize the majorization minimization (MM) method to solve the proposed optimization model. It is interesting to note that at each iteration a quadratic optimization problem is formulated and its analytical solution can be achieved, thereby making the proposed algorithm effective. Extensive experiments on face images demonstrate that our method achieves better performance than some previous methods.