Abstract: Gromov-Wasserstein distance is proposed as a new method to perform shape matching in order to improve the precision and matching rate. First, the two shapes are embedded into the metric measure space. Based on G-W distance, the objective function and constraint condition can be constructed after generating samples via farthest points sampling. This is a NP-hard QAP problem. In order to solve the problem, we propose a group of linear systems via the constraint relaxation to get the solution, after conducting the projected gradient approach, which is more accurate and greatly closer to the theoretical value. This can satisfy the matching precision and improve the matching rate. Experimental results on the SHER'10 data set demonstrate that our method is superior than state-of-the-art methods.