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Graph matching plays an important role in many fields in computer vision. It is a well-known general NP-hard problem and has been investigated for decades. Among the large amount of algorithms for graph matching, the algorithms utilizing the path following strategy exhibited state-of-art performances. However, the main drawback of this category of algorithms lies in their high computational burden. In this paper, we propose a novel path following strategy for graph matching aiming to improve its computation efficiency. We first propose a path estimation method to reduce the computational cost at each iteration, and subsequently a method of adaptive step length to accelerate the convergence. The proposed approach is able to be integrated into all the algorithms that utilize the path following strategy. To validate our approach, we compare our approach with several recently proposed graph matching algorithms on three benchmark image datasets. Experimental results show that, our approach improves significantly the computation efficiency of the original algorithms, and offers similar or better matching results.