The growing popularity of storing large data graphs in cloud has inspired the emergence of subgraph pattern matching on a remote cloud, which is usually defined in terms of subgraph isomorphism. However, it is an NP-complete problem and too strict to find useful matches in certain applications. In addition, there exists another important concern, i.e., how to protect the privacy of data graphs in subgraph pattern matching without undermining matching results. To tackle these problems, we propose a novel framework to achieve the privacy-preserving subgraph pattern matching via strong simulation in cloud. Firstly, we develop a k-automorphism model based method to protect structural privacy in data graphs. Additionally, we use a cost-model based label generalization method to protect label privacy in both data graphs and pattern graphs. Owing to the symmetry in a k-automorphic graph, the subgraph pattern matching can be answered using the outsourced graph, which is only a subset of a k-automorphic graph. The efficiency of subgraph pattern matching can be greatly improved by this way. Extensive experiments on real-world datasets demonstrate the high efficiency and effectiveness of our framework.