The hierarchical dual-net (HDN) was introduced as a topology of interconnection networks for extremely large parallel computers. The HDN is constructed based on a symmetric product graph (base network). A k-level hierarchical dual-net, HDN(B, k, S), contains (2N0)2k /(2 ×􏰂Π􏰂ki=1 si) nodes, where S = {G′1, G′2, . . . , G′k}, G′i is a super-node and si = |G′i| is the number of nodes in the super-node at the level i for 1 ≤ i ≤ k, and N0 is the number of nodes in the base network B. The node degree of HDN(B, k, S) is d0 + k, where d0 is the node degree of the base network. The HDN is node and edge symmetric and can contain huge number of nodes with small node-degree and short diameter. Disjoint-path routing is a fundamental and critical issue for the performance of an interconnection network. In this paper, we propose an efficient algorithm for finding disjoint-paths on an HDN and give the performance simulation results.