To improve the accuracy of damage identification, the concept of reciprocal variables is introduced, and a truss damage identification method combining reciprocal variables with the generalized flexibility matrix is proposed. This method requires only low-order modal parameters. For cases of incomplete measured mode shapes, a control equation based on incomplete mode shapes is introduced, and an iterative strategy based on the non-negative least squares method is employed to solve the damage identification problem. In each iteration cycle, this iterative method utilizes the non-negative least squares method to determine the location and extent of structural damage, reconstructs a new coefficient matrix by excluding undamaged elements, and proceeds to the next cycle of solution using the new coefficient matrix and the original right-hand side term until the convergence accuracy requirement is satisfied. Numerical simulation results demonstrate that, compared with the original identification method based on the generalized flexibility matrix, the method combining reciprocal variables with the generalized flexibility matrix achieves superior identification performance. Under conditions of noise and incomplete measured mode shapes, the method combining the incomplete mode shape control equation with the aforementioned iterative strategy can maintain a certain level of identification accuracy.