As the traffic grows rapidly in the Internet, the QoS (Quality of Service) guarantee of the flows and the traffic engineering problems have become very important issues. MPLS (MultiProtocol Label Switching) has more advantages to solve the problems than existing IP routing because of more free using of multiple paths between the source and destination pairs. Particularly the availability of Constraint-based Routing and explicit route in MPLS made the problems referred above solved efficiently. But the CSPF algorithm used in Constraint-based Routing has the characteristic that it selects the shortest path of all paths which meet the traffics’ QoS constraints. So, even though Best-effort traffic which is only routed to the shortest path can be routed to alternative path, it is dropped by the intermediate nodes during congestion period. Therefore, if we reroute the best-effort traffic to the alternative path when congestion happens, the network resource could be used efficiently and the load on intermediate router in the path can be less. In this paper, we present the modified cost function used in path computation for best-effort traffic and verify that the using of that cost function make traffic engineering more effective through simulation.