Graph matching is important in pattern recognition and computer vision which can solve the point correspondence problems. Graph matching is an NP-hard problem and approximate relaxation methods are used to solve this problem. But most of the existing relaxation methods solve graph matching problem in the continues domain without considering the discrete constraints. In this paper, we propose a fast normalized cut based graph matching method which takes the discrete constraints into consideration. Specifically, a regularization term which is related to the discrete form of the permutation matrix is added to the objective function. Then, the objective function is transformed to a form which is similar to the fast normalized cut framework. The fast normalized cut algorithm is generalized to get the permutation matrix iteratively. The comparisons with the state-of-the-art methods validate the effectiveness of the proposed method by the experiments on synthetic data and image sequences