Abstract Graph matching is a fundamental problem in computer vision and pattern recognition area. In general, it can be formulated as an Integer Quadratic Programming (IQP) problem. Since it is NP-hard, approximate relaxations are required. In this paper, a new graph matching method has been proposed. There are three main contributions of the proposed method: (1) we propose a new graph matching relaxation model, called Binary Constraint Preserving Graph Matching (BPGM), which aims to incorporate the discrete binary mapping constraints more in graph matching relaxation. Our BPGM is motivated by a new observation that the discrete binary constraints in IQP matching problem can be represented (or encoded) exactly by a ℓ2-norm constraint. (2) An effective projection algorithm has been derived to solve BPGM model. (3) Using BPGM, we propose a path-following strategy to optimize IQP matching problem and thus obtain a desired discrete solution at convergence. Promising experimental results show the effectiveness of the proposed method</