With the popularity of cloud computing, cloud outsourcing has aroused great concern in academia. A lot of graph data are outsourced to the cloud for saving cost. As the cloud server may be not entirely reliable, the outsourced graph data are usually encrypted before sending to the cloud for the security considerations. Adjacency search is a basic operation, and many other operations can be performed based on the adjacency search. Adjacency search supporting synonym query is a more meaningful operation which can make a query user improve the scope of the query. Due to the graph data being encrypted in the cloud, adjacency search supporting synonym query becomes a very challenging task. In this paper, we propose an efficient solution to perform privacy-assured adjacency search supporting synonym query on the encrypted graph in the cloud (PASQ). Our work utilizes a stemming algorithm and an encryption mechanism to perform adjacency search. A query user can get a wider range of search results by this solution, and the privacy of query will not be disclosed. We present a design scheme for the outsourced graph and analyze the security. We demonstrate the efficiency of our scheme by the experiment results on a real graph data.