Abstract Due to the efficiency of representing visual data and reducing dimension of complex structure, methods of sparse coding have been widely investigated and achieved ideal performance in image classification. These sparse coding methods learn both a dictionary and the sparse codes from the original data together under the constraint to l1-norm. However, the introduction of l1-norm tends to choose small number of atoms from the relevant bases in process of dictionary learning, abandoning other high-related bases, which results in the neglect of group effect and weak generalization of the model. In this paper, we propose a novel sparse coding model which introduces the l2-norm constraint and the second-order Hessian energy in the optimization function. This model eliminates the restrictions on the number of selected base vectors in the dictionary learning, and makes better use of the topological structure information as well, thus the intrinsic geometric characteristics of the data is described more accurately. In addition, our model is extended with a non-negative local constraint, which ensures similar features to share their local bases. Extensive experimental results on the real-world datasets show that the proposed model extraordinarily outperforms several state-of-the-art image representative methods.