Abstract: In order to improve sparsity and robustness, a novel sparse penalty function based on smoothly clipped absolute diviation (SCAD) is proposed and applied to Lagrange Constraint Neural Network (LCNN). This method can solve ill-conditioned problem and improve sparsity, stability, and accuracy in blind image restoration. Both artificial and real-world data are calculated under some different restoration methods. Results of the experiments show that Lagrange constraint neural network with sparse penalty has better restoration effect.