We propose a new QOS routing algorithm for finding a path that guarantees several quality of service (QOS) parameters requested by users, for ATM networks. It is known that a routing problem is NP-complete, if the number of additive QOS parameters, such as delay and cost, are more than or equal to two. Although a number of heuristic algorithms have been proposed recently to solve this problem, the appropriate choice of routing algorithms is still an open issue. In this paper, we propose a new heuristic routing algorithm, while being compliant with PNNI routing and signaling specification in the ATM Forum. The performance of algorithms is evaluated by simulation with a various network topologies and loading scenarios. This simulation results demonstrate that the proposed scheme improves the performance while reducing computational complexity.