This paper proposes a sparse coding algorithm based on KKT conditions.Firstly,the non-convex non-smooth sparse coding problem is decomposed into two convex non-smooth problems.Secondly,the two convex non-smooth problems are skillfully transformed into three smooth convex optimization problems by using two matrices.Finally,the three problems are solved by KKT conditions.In addition,we prove the convergence of the algorithm.Meanwhile,experimental simulation shows the convergence of the algorithm.