In this paper, we propose a novel limited path algorithm called LPUA to deal with two constrained unicast QoS routing problems, which is known as NP complete. By combining two weights linearly into a single one, Dijkstra algorithm based on the single weight can be used directly to return a least cost path between the source node and the destination node. When a routing request comes, LPUA only needs to compute a limited number of paths. If any of these paths cannot meet the routing constraints, the routing request would be refused. Extensive simulations have show that LPUA is very efficient.