We suggest a novel approach to the sparse covariance matrix estimation (SCME) problem using the ℓ1-norm. The resulting optimization problem is nonconvex and very hard to solve. Fortunately, it can be reformulated as DC (Difference of Convex functions) programs to which DC programming and DC Algorithms can be investigated. The main contribution of this paper is to propose a more suitable DC decomposition for solving the SCME problem. The experimental results on both simulated datasets and two real datasets in classification problem illustrate the efficiency of the proposed algorithms.