Recently, the TPR-tree has been proposed to support spatio-temporal queries for moving objects. Subsequently, various methods using the TPR-tree have been intensively studied. However, although the TPR-tree is one of the most popular access methods in spatio-temporal databases, any cost model for the TPR-tree has not yet been proposed. Existing cost models for the spatial index such as the R-tree do not accurately ostinato the number of disk accesses for spatio-temporal queries using the TPR-tree, because they do not consider the future locations of moving objects. In this paper, we propose a cost model of the TPR-tree for moving objects for the first time. Extensive experimental results show that our proposed method accurately estimates the number of disk accesses over various spatio-temporal queries.