Researches on the method of the performance evaluation of government investment in public project are mainly embodied in indicator system. However, these models do not attach importance to the applicability. So, it causes lack of suitable evaluation model for evaluating the projects of government investment in public project in Low-Carbon Economy. Therefore, this article in accordance with the characteristics of this investment in public projects, combined the gray relational analysis method, fuzzy comprehensive evaluation method and stepwise discriminate analysis method with their respective advantages to develop a new algorithm——GFS algorithm. Using the GFS algorithm can do discriminate analysis for a new investment project. Practice shows that the GFS algorithm has a good effect. It can provide the theoretical basis for decision-making of senior government managers.