A fast iterative algorithm for solving the eigenvalue perturbation problem is proposed in this paper for solving the problem of slow convergence of traditional methods for eigenvalue perturbation calculation. Firstly， the eigenvalue perturbation problem of the initial matrix is transformed into the eigenvalue perturbation problem of the diagonal matrix by matrix transformation. Then， a fast iterative algorithm is proposed to solve the perturbation parameter. The convergence of the algorithm is analyzed and compared with the method derived based on the perturbation series expansion method， and the strategy of solving the eigenvalues one by one and reducing the order of the matrix is adopted to effectively reduce the computation cost. Finally， two examples are used to show the calculation process of the algorithm and its application in the tracking of modal parameters of vibration structures.