Location privacy has been a hot topic in recent years. However, the methods of existing location privacy preserving only support simple nearest neighbor queries, which do not consider the obstructed space. But in fact, the obstructed space is very popular in our life. Therefore, we study location privacy preserving obstructed nearest neighbor queries. Due to the effect of obstacles, this problem is also very hard. In this paper, we adopt a normal approach based on the third trusted party for privacy preserving obstructed nearest neighbor (ONN) queries. The approach can entertain the location-based service without leaking the user's exact location and obtain the exact answer. In our approach, firstly, the third trusted party constructs a cloaked region corresponding to the exact location and sends the cloaked region to the LBS. Then LBS processes the query region. In the process of query processing, we use two methods to return a set of candidate answers with respect to the cloaking region for the actual user location: 1)Basic approach of query processing, which uses the max obstructed distance of segment to expand the region and returning the results in the expanded region; 2)Improved approach of query processing, which further narrows the expanded region based on the basic approach. At last, the third trusted party returns the actual answer to the users corresponding to user's exact location .Finally, experimental results and proof theory show the effectiveness and correctness of our approach.