The structural damage identification through modal data often leads to solving a set of linear equations. Special numerical treatment is sometimes required for an accurate and stable solution owing to the ill conditioning of the equations. Based on the singular value decomposition (SVD) of the coefficient matrix, an error based truncation algorithm is proposed in this paper. By rejection of selected small singular values, the influence of noise can be reduced. A simply-supported beam is used as a simulation example to compare the results to other methods. Illustrative numerical examples demonstrate the good efficiency and stability of the algorithm in the nondestructive identification of structural damage through modal data. The structural damage identification through modal data often leads to solving a set of linear equations. matrix, an error based truncation algorithm is proposed in this paper. By rejection of selected small singular values, the influence of noise can be reduced. A simply-supported beam is used as a simulation example to compare the results to other methods. examples demonstrate the good efficiency and stability of the algorithm in the nondestructive identification of structural damage through modal data.