An algorithm of the optimal measurement placement is proposed for the material parameter identification of two-dimensional orthotropic composites, which is modeled by the finite element. From the analysis of the system sensitivity matrix of the parameter identification processes using the Levenberg-Marquardt method, A-optimality criterion related with the Fisher Information Matrix (FIM) is selected for the criterion of the optimal measurement placement. Thus, the algorithm for selecting the optimal measurement placement can be constructed. A numerical example is given to demonstrate the effectiveness of the proposed algorithm. The example reveals that the measurement placement has a significant influence on the identification results.