The characteristics of tile self-assembly model are nanoscale properties, self-assembly, programmable and so on, so it has a great advantage in solving NP problems. This paper proposed a new tile self-assembly model for maximum matching problem. The new model is composed of initial configuration subsystem, choosing subsystem and detecting subsystem. In the new model DNA tiles were designed to store the information. The solution space of maximum matching problem was generated through the assembly operation. Lastly, the answers were found out by the detecting tiles. The performance of the algorithm was also analyzed in terms of the assembly time, the computation space and the types of the tiles, and the algorithm was simulated to prove its effectiveness and correctness.