A best matrix approximation technique for updating the analytical model is developed using the known modal parameters. Firstly, the known modal matrix is decomposed by means of the singular-value decomposition technique. Secondly, the general updating equations for the analytical model are obtained on the basis of the singular-value decomposition results, the eigenequation, and the modal orthogonality relations. Thirdly, the best updating solution is defined according to the best approximation theory, and the existence and uniqueness of the best modification results relative to the analytical model are studied. Finally, the concrete form of the best modification and two updating algorithms are presented. Numerical examples demonstrate that the proposed method possesses high modificatory accuracy compared with some other methods, and it possesses the ability to modify larger error models.