The problems in computer vision of finding the global correspondences across a set of images can be formulated as a multiple graph matching problem consisting of pairwise matching problems. In the multiple graph matching problem, matching consistency is as important as matching accuracy for preventing the contrariety among matched results. Unfortunately, since the majority of conventional pairwise matching methods only approximate the original graph matching problem owing to its computational complexity, a framework that separately matches each graph pair could generate inconsistent results in practical environments. In this paper, we propose a novel multiple graph matching method based on the second-order consistency concept, which simultaneously considers the matching information of all possible graph pairs. We reformulate the multiple graph matching problem to encourage second-order consistency and design an iterative optimization framework. In our experiments, the proposed method outperforms state-of-the-art methods in terms of both consistency and accuracy.