Abstract: PPP project mode has been widely-used in many fields, such as transportation, housing construction, energy, education, etc. In order to better realize the friendly cooperation between the government and social enterprises, this paper studies the matching selection between the government and social enterprises based on two-sided matching theory. According to the on-site inspection and literature analysis, the evaluation index system of social enterprise to government and government to social enterprise in PPP project was established respectively. The grey relational analysis method was introduced to deal with the evaluation information of evaluation indexes between government and enterprises, and the weight of each evaluation index was obtained by using BWM, so as to build a two-sided fair matching model with the greatest satisfaction between government and enterprises. Through the example analysis, the model was applied to the government enterprise matching of PPP project, and the feasibility and effectiveness of the proposed method were verified.