As a policy-based routing protocol, BGP (border gateway protocol) allows each AS to choose local routing policy independently. Possible policies conflict may result in BGP route persistent oscillation. This paper proposes an adaptive mechanism to guarantee BGP convergence with policies conflict, which neither impairs the flexibility of choosing routing policy, nor inserts additional information in BGP messages. With the mechanism, route stability is taken into BGP decision process so that unstable route is degraded to cause more stable route to be chosen to stop policies dispute. The new mechanism also can adapt to topology change and converge to new stable route.