Searching local graph clusters is an important problem in big network analysis. Given a query node in a graph, local clustering aims at finding a subgraph around the query node, which consists of nodes highly relevant to the query node. Existing local clustering methods are based on single networks that contain limited information. In contrast, the real data are always comprehensive and can be represented better by multiple connected networks (multi-network). To take the advantage of heterogeneity of multi-network and improve the clustering accuracy, we advance a strategy for local graph clustering based on Multi-network Random Walk with Restart (MRWR), which discovers local clusters on a target network in association with additional networks. For the proposed local clustering method, we develop a localized approximate algorithm (AMRWR) on solid theoretical basis to speed up the searching process. To the best of our knowledge, this is the first elaboration of local clustering on a target network by integrating multiple networks. Empirical evaluations show that the proposed method improves clustering accuracy by more than 10% on average with competently short running time, compared with the alternative state-of-the-art graph clustering approaches.