We address the correspondence search problem among multiple graphs with complex properties while considering the matching consistency. We describe each pair of graphs by combining multiple attributes, then jointly match them in a unified framework. The main contribution of this paper is twofold. First, we formulate the global correspondence search problem of multi-attributed graphs by utilizing a set of multi-layer structures. The proposed formulation describes each pair of graphs as a multi-layer structure, and jointly considers whole matching pairs. Second, we propose a robust multiple graph matching method based on the multi-layer random walks framework. The proposed framework synchronizes movements of random walkers, and leads them to consistent matching candidates. In our extensive experiments, the proposed method exhibits robust and accurate performance over the state-of-the-art multiple graph matching algorithms.