PACS 89.75.Fb -Structures and organization in complex systems PACS 05.10.-a -Computational methods in statistical physics and nonlinear dynamics PACS 02.20.-a -Group theory Abstract -It is a challenging work to assess research performance of multiple institutes. Considering that it is unfair to average the credit to the institutes which is in the different order from a paper, in this paper, we present a credit allocation method (CAM) with a weighted order coefficient for multiple institutes. The results for the APS dataset with 18987 institutes show that top-ranked institutes obtained by the CAM method correspond to well-known universities or research labs with high reputation in physics. Moreover, we evaluate the performance of the CAM method when citation links are added or rewired randomly quantified by the Kendall's Tau and Jaccard index. The experimental results indicate that the CAM method has better performance in robustness compared with the total number of citations (T C) method and Shen's method. Finally, we give the first 20 Chinese universities in physics obtained by the CAM method. However, this method is valid for any other branch of sciences, not just for physics. The proposed method also provides universities and policy makers an effective tool to quantify and balance the academic performance of university.