Interconnection networks play a crucial role in the performance of massively parallel computers. Hierarchical interconnection networks provide high performance at low cost by exploring the locality that exists in the communication patterns of massively parallel computers. A Hierarchical Torus Network (HTN) is a 2D-torus network of multiple basic modules, in which the basic modules are 3D-torus networks that are hierarchically interconnected for higher level networks. The static network performance of the HTN has already been studied and has been shown to be good. Dynamic communication performance has been evaluated under uniform traffic pattern but not under non-uniform traffic patterns. In this paper, we present a deadlock-free routing algorithm for the HTN using 3 virtual channels and evaluate the network's dynamic communication performance under three non-uniform traffic patterns, using the proposed routing algorithm. We evaluate the dynamic communication performance of HTN, H3D-mesh, H3D-torus, TESH, and mesh networks by computer simulation. We find that the dynamic communication performance of HTN is better than that of the H3D-mesh, H3D-torus, TESH, and mesh networks.