ObjectRank is a method of link structure analysis to evaluate the importance of objects in a database. ObjectRank is known to be computationally expensive, because it requires iterative computations over a large graph. However, in many real applications, it is sufficient to compute the ObjectRank scores for only small fraction of objects. To address this problem, this paper proposes a novel method for estimating ObjectRank scores for specific objects by applying local computation over partial graphs, thereby allowing us to maintain low computational cost even for large graphs. Our basic idea is that, for a given target node, we induce a local graph by checking the edge weights and pruning the edges with considering their weights. We conduct experiments to compare our method with some comparative methods. The experimental results show that our method can reduce the computational cost while maintaining the accuracy.