Achieving a network structure with optimal synchronization is essential in many applications. This paper proposes an optimization algorithm for constructing a network with optimal synchronization. The introduced algorithm is based on the eigenvalues of the connectivity matrix. The performance of the proposed algorithm is compared with random link addition and a method based on the eigenvector centrality. It is shown that the proposed algorithm has a better synchronization ability than the other methods and also the scale-free and small-world networks with the same number of nodes and links. The proposed algorithm can also be applied for link reduction while less disturbing its synchronization. The effectiveness of the algorithm is compared with four other link reduction methods. The results represent that the proposed algorithm is the most appropriate method for preserving synchronization.