Because of the successful use of the sparse representation in face classification algorithm, a more efficient classification method based on Sparse Representation-based pattern Classification (SRC) and elastic network was proposed. To enhance the ability of collaborative representation and enhance the ability to deal with strongly correlated data, a sparse decomposition method based on elastic network was proposed based on the iterative dynamic culling mechanism. Test samples were represented by a linear combination of training samples, and the iterative mechanism was used to remove the categories and samples with less contribution to the classification from all the samples, the Elastic Net algorithm was used for coefficient decomposition to select the samples and classes with high contribution to the classification. Finally, the test samples were classified according to the similarity. The experiment results show that the recognition rate of the algorithm is 98.75%, 86.62% and 99.72% respectively for the ORL, FERET and AR data sets which shows the effectiveness of the proposed algorithm. Compared with the methods of LASSO and SRC-GS, the proposed algorithm can enhance the ability of dealing with high-dimension small sample and strongly correlated variable data in the process of coefficient decomposition. It highlights the importance of sparse constraint in the algorithm and has higher accuracy and stability, and can be more effectively applied to face classification.