A range $Top-kappa$ query returns top k records in order of a measure attribute within a specified region on multi-dimensional data, and it is a powerful tool for analysis in spatial databases and data warehouse environments. In this paper, we propose an algorithm for answering the query via selective traverse of a Hierarchical Max R-Tree(HMR-tree). It is possible to execute the query by accessing only a small part of the leaf nodes in the query region, and the query performance is nearly constant regardless of the size of the query region. The algorithm manages the priority queue efficiently to reduce cost of handling the queue and the proposed HMR-tree can guarantee the same fan-out as the original R-tree.