Using the eigenvalue problem of damaged structure, the BFGS perturbation method is constructed to detect the damage situation of a fixed beam. Damaged locations and their extents of fixed-fixed beam with multiple elements can be accurately obtained in a few iterations using several vibration modes. First, perturbation expansions of the stiffness matrix, eigenvalue and eigenvector perturbation equations of the damaged structure are carried out and will be substituted into the eigenvalue equation of the damaged structure. Then, eigen-parameter p-th order perturbation terms of all orders are derived explicitly and directly by gathering p-th elastic modulus perturbed terms. Finally, by substituting the perturbation terms into the perturbation equations, multiple elastic moduli are optimized using the BFGS quasi-Newton iteration. Its objective function is generated from the summation of the remaining terms in the perturbation equation. Using the finite element model of fixed-Fixed beam, the applicability of the algorithm under limited modes and reduced-rder models is validated by damage detections on the five o nine elements beam. In termination criterion aspect, convergences of different iteration statuses are compared using d-norm and t-norm indicators. Various element numbers and their damage extents are accurtely detected with 0.06 to 0.001 elastic modulus errors.