Cloud computing enables the users to outsource and access data economically from the distributed cloud server. Once the data leaves from data owner premises, there is no privacy guarantee from the untrusted parties in cloud storage system. Providing data privacy for the outsourced sensitive data is a challenging task in cloud computing. In this paper we have proposed a Trusted Third party Query Process(TTQP) method to provide data privacy for graph structured outsourced data. This method utilize the encrypted graph frequent features search index list to search the matched query graph features in graph data base. The proposed system has analyzed in terms of different size of data graphs, index storage, query feature size and query execution time. The performance analysis of our proposed system shows, this method is more secure than the existing privacy preserving encrypted Query Graph (PPQG).