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In this paper, we propose a parallel and distributed routing algorithm for the ATM/B-ISDN transport networks. In the proposed routing algorithm, a hierarchical connection management architecture is used where each subnetwork has its own connection management functions to find the shortest path for the requested subnetwork connections and the routing information is merged by the upper-level domain subnetwork to find the shortest path in the merged domain of upper-level. This subnetwork routing is performed in each subnetwork in hierarchy, providing maximized parallel and distributed processing capability. The proposed parallel and distributed routing algorithm can reduce the routing and connection setup time in a large-scale network, such as a public B-ISDN.