Database users may be frustrated by no answers returned when they pose a query on the database. In this paper, we study the problem of relaxing queries on RDF databases in order to acquire approximate answers. We address two problems in efficient query relaxation. First, to ensure the quality of answers, we compute the similarities between relaxed queries with regard to the user query and use them to score the potential relevant answers. Second, for obtaining top-k answers, we develop two algorithms. One is based on the best-first strategy and relaxed queries are executed in the ranking order. The batch based algorithm executes the relaxed queries as a batch and avoids unnecessary execution cost. At last, we implement and experimentally evaluate our approaches.